The solution of the inequality is greater than or equal to 18. The number of fruit snacks that were in the bag is 18.
What is the inequality?
In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given inequality is
X÷3 ≥ 6
Rewrite left side expression:
X/3 ≥ 6
Multiply both sides by 3:
X ≥ 6 × 3
X ≥ 18
The value X is greater than or equal to 18.
Therefore the number of fruit snacks that were in the bag is 18.
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A side of the equilateral triangle 'A' is twice the length of a side of
another equilateral triangle 'B'. How many triangles of 'B' will fit
into triangle 'A'?​
Total four triangles of B fit into triangle A as length of the equilateral triangle A is twice the length of triangle B.
As given in the question,
Types of triangles : Equilateral triangle
Number of triangle = 2
Triangle A and Triangle B
Let 'x' be the length of the triangle A
And 'y' be the length of the triangle B
As per given condition:
x = 2y
Area of equilateral triangle A = (√3/4)x²
Area of equilateral triangle B = (√3/4)y²
Now x = 2y
⇒Area of equilateral triangle A = (√3/4)(2y)²
⇒Area of equilateral triangle A = (√3/4)4y²
⇒Area of equilateral triangle A = 4 [(√3/4)y²]
⇒Area of equilateral triangle A = 4 ( area of equilateral triangle B)
Therefore, total number of four equilateral triangle of B fit into equilateral triangle A.
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for the range c6:c41, create a new conditional format that changes the font color to red for values that are greater than or equal to 50.
The following steps would apply conditional formatting to the range:
Select the range of cells C6 : C41Click Conditional Formatting on the Home tabSet the conditionPoint to Color Scales, and then select the font color as red colorHow to apply the conditional formatting?The given parameters in the question are:
Range = C6 : C41Condition = cell that are greater than or equal to 50.Action = font color as red colorThe Conditional Formatting is located on the home tab
So, the first step to select the range and locate the Conditional Formatting option
Then set the necessary conditions and formats
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The area of a rectangle is 35 m², and the length of the rectangle is 3 m more than double the width. What is the dimensions of the rectangle?
The dimensions of the rectangle with area 35 m² is
length = 7.6 m and width = 4.6 m
How of find the dimension of the rectangleThe dimension of the rectangle is calculated using the formula for area of rectangle
= length x width
where
length = 3 + w width = warea of rectangle
35 = (w + 3) * w
35 = w² + 3w
w² + 3w - 35 = 0
solving for w gives
w = 4.6 OR -7.6
using the positive value, the w = 4.6 m, l = 4.6 + 3 = 7.6 m
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l
look at the picture
The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains all the ordered pairs outside the parabola.
What is parabola?
A parabola could be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a fixed line that is understood because the directrix.
Main body:
In this problem we must determine a quadratic inequality of the form:
a · x² + b · x + c < y
Where a, b, c are the real coefficients of the inequality.
First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:
25 · a - 5 · b + c = 0
4 · a + 2 · b + c = 0
a + b + c = - 18
(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)
Second, write the quadratic in equation:
(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
hence , the equation is (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y
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If the slant height of a triangular face of a square based pyramid of side
16cm is 17cm, find the volume of the pyramid.
Answer must be 1280 cube cm
Answer:
1280 cm³
I presume you are looking for the solution steps and these are below
Step-by-step explanation:
If the each side of the square pyramid is 16 and the slant height is 17, then the height of the pyramid, half the side and the slant edge form a right triangle.
The height of the pyramid can be computed using the Pythagorean theorem
Let a be each side, h the height and s the slant height
[tex]s^2 = h^2 + (a/2)^2\\\\\\s^2 = h^2 + \dfrac{a^2}{4}\\\\\textrm{Plugging in known values,}\\17^2 = h^2 + \dfrac{16^2}{4}\\\\289= h^2 + 64\\\\h^2 = 289 - 64\\\\h^2 = 225\\\\h = \sqrt{225} = 15\\\\[/tex]
The volume, V of a square pyramid of side a and height h is given by the formula:
[tex]V = \dfrac{1}{3}a^2h\\\\\\\textrm{Plugging in values,}\\\\V = \dfrac{1}{3}\cdot 16^2 \cdot 15\\\\[/tex]
[tex]V = \dfrac{1}{3} \cdot 256 \cdot 15\\\\V = 256 \cdot 5\\\\V = 1280[/tex]
The volume of the pyramid is 1280 cubic cm.
Given the slant height of the pyramid is 17 cm and the length of square base of the pyramid is 16 cm.
Now we know the volume of the pyramid with a square base = [tex]\frac{1}{3}[/tex]×area of the base×height.
So we need the values for area of the base and height of the pyramid.
Area of the square base=16×16 sq. cm.= 256 sq. cm.
Again we can apply the relation to find the value of height,
(Slant height)² = (Height)² + ([tex]\frac{1}{2}[/tex]×Length of the base)²
So, putting the values we get,
[tex](17)^2 = (height)^2 +(\frac{16}{2})^2[/tex]
⇒ [tex]289 = (height)^2+64[/tex]
⇒ [tex](height)^2= 225[/tex]
⇒ [tex]height = 15cm[/tex]
Now by appyling the volume of the pyramid we get,
Volume = [tex]\frac{1}{3} \times 256 \times 15[/tex] cubic cm. = 1280 cubic cm.
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How do type an exponent on a chromebook laptop?
Step-by-step explanation:
Press ''CTRL + /'' to access the list of features.
Find the “Text Formatting” section.
Choose “Superscript” from the list of options.
On the right-hand side, you'll see the ''CTRL +. '' shortcut. Use it to make the number or letter in your text appear in exponent form.
Step-by-step explanation:
1. Place your cursor where you want an exponent. For example, if you want to place an exponent after the number 10 in a document, place your cursor directly after the 10 with no space.
2. Type Alt+0185 for the exponent 1. For example, you can type the number 10¹ holding the Alt key and typing 0185.
3. Type Alt+0178 for the exponent 2. For example, you can type the number 10² holding the Alt key and typing 0178.
4. Type Alt+0179 for the exponent 3. For example, you can type the number 10³ by holding the Alt key and typing 0179.
can someone help i will give brainlest:)
A. Width = 16.5 ft B.Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
The formula for Area of rectangle:The area of the rectangle is a place covered by a rectangle in a 2D plane
The formula for Area of the rectangle is given by
Area = Length × WidthHere we have
1 in = 3 feet and 1 cm = 6.5 ft
Calculation for rectangle A :
In rectangle A
Width = 5.5 in
=> Width in feet = 5.5 × 3 feet = 16.5 ft
Height = 3.1 in
=> Height in feet = 3.1 × 3 feet = 9.3 ft
By the given formula
Area = 16.5 ft × 9.3 ft = 153.45 ft²
Calculation for rectangle B :
In rectangle B
Width = 8.5 cm
=> Width in feet = 8.5 × 6.5 feet = 55.25 ft
Height = 14 cm
=> Height in feet = 14 × 6.5 feet = 91 feet
By the given formula
Area = 55.25 ft × 91 ft = 5027.75 ft²
Therefore,
A. Width = 16.5 ft B. Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
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There are a total of 58 reindeer and elves helping Santa get ready for Christmas. Each reindeer has 4 legs and each elf has 2 legs. Frosty the Snowman, who doesn’t have any legs, counted 158 legs when all the reindeer and elves were in Santa’s workshop helping Santa. How many elves are helping Santa? Enter your answer as a number only.
Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.
How many elves are helping Santa?
Let's define the variables:
x = number of elves.y = number of reindeer.We know that there are 58 of them, then we can write:
x + y = 58
We also know that between all of them they have 158 legs, so we can write the equation:
x*2 + y*4 = 158
Then the system of equations is:
x + y = 58
x*2 + y*4 = 158
To solve this system of equations, we can isolate x on the first equation to get:
x = 58 - y
Replacing that in the other equation we will get:
(58 - y)*2 + y*4 = 158
Now we can solve this equation for y.
(58 - y)*2 + y*4 = 158
116 - 2y + 4y = 158
116 + 2y = 158
2y = 158 - 116
2y = 42
y = 42/2
y = 21
Then the value of x is:
x = 58 - y
x = 58 - 21
x = 37
there are 37 elves.
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What is ab as shown in the attached question
Answer:
(c) -42
Step-by-step explanation:
You want the product ab given that ...
f(x) = 3x³ +ax² -5x +7g(x) = -3x⁴ +2x³ +3x² +bx +12(f+g)(x) = -3x⁴ +5x³ +9x² -12x +19Comparing coefficientsThe function (f+g)(x) is the sum of the other two functions. For the purpose here, we only need to look at terms that involve 'a' and 'b'.
Comparing coefficients of x², we have ...
ax² +3x² = 9x²
a = 9 -3 = 6
Comparing coefficients of x, we have ...
-5x +bx = -12x
b = -12 +5 = -7
The product is ...
ab = (6)(-7) = -42
Quadrilateral ABCD is translated to get quadrilateral A′B′C′D′. Vertex A is at (-5, 2), and vertex A′ is at (2, -2).
Quadrilateral ABCD is translated
. If vertex B is at (-6, 5), then vertex B′ is at
The vertex B' is at (1, 1)
How to find the calculation?Let's update the guidelines for translating a point.
The image of the point (x, y) is (x + h, y) T (x, y) (x + h, y) if the point (x, y) is translated horizontally to the right by h units.The image of the point (x, y) is (x - h, y) T (x, y) if the point (x, y) is translated horizontally to the left by h units (x - h, y)The image of the point (x, y) is (x, y + k) (x + h, y) T (x, y) (x, y + k) if the point (x, y) is translated vertically up by k units.The image of the point (x, y) is (x, y - k) T (x, y) if the point (x, y) is translated down vertically by k units (x, y - k)Let's apply the guidelines to resolve our issue.
Vertex A equals (-5, 2)
Vertex A' equals (2, -2)
The two points' coordinates changed, indicating that the
horizontal and vertical translations of a quadrilateral
A's x-coordinate is equal to -5.
A' has an x-coordinate of 2
Which indicates it goes to the right, therefore adhere to the first guideline presented above.
The translation formula is T (x, y) (x + h, y).
∴ x → x + h
x = -5, and x + h = 2.
∴ -5 + h = 2
Increase both sides by 5.
∴ -5 + 5 + h = 2 + 5
∴ h = 7
∴ The quadrilateral is moved seven units to the right.
A has a y-coordinate of 2
A"s y-coordinate is equal to -2.
Which means it descends, therefore apply the fourth rule listed above.
T (x, y) is the translational rule (x, y - k)
∴ y → y - k
Because y = 2 and y - k = -2,
∴ 2 - k = -2
Increase K on both sides.
∴ 2 - k + k = -2 + k
∴ 2 = -2 + k
Increase both sides by 2.
∴ 2 + 2 = -2 + 2 + k
∴ 4 = k
The quadrilateral is down four units.
Let's locate B.
T (x, y) (x + h, y - k) is the translational rule.
∵ B = (-6, 5) (-6, 5)
∵ h = 7 and k = 4
∴ B' = (-6 + 7, 5 - 4)
∴ B' = (1, 1) (1, 1)
Vertex B is located at (1, 1).
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Rather than being irrelevant or unhelpful, residuals in a simple linear regression model can be quite informative. Which of the following, in your opinion, residuals might indicate about the underlying population and the model?
Regression analysis will indicate about the underlying population and the model.
It is one of the most used and most powerful multivariate statistical techniques for it infers the existence and form of a functional relationship in a population. Once you learn how to use regression, you will be able to estimate the parameters { the slope and intercept } of the function that links two or more variables. With that estimated function, we will be able to infer or forecast things like unit costs, interest rates, or sales over a wide range of conditions.
Though the simplest regression techniques seem limited in their applications, statisticians have developed a number of variations on regression that greatly expand the usefulness of the technique. And again, the t-distribution and F-distribution will be used to test hypotheses.
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The measures of the angles of a triangle are shown in the figure below. Solve
for X.
Answer:
x = 4
Step-by-step explanation:
The sum of the interior angles of a triangle equal 180.
2x + 15 + 67 + 90 = 180 Combine like terms
2x + 172 = 180 Subtract 172 from both sides
2x + 1752 - 172 = 180 - 172
2x = 8 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]
x = 4
Answer:
x= 4
Step-by-step explanation:
To Find: Angle Measure X67+2x+15+90=180 (Sum of measures of a Triangle)
2x + 172 = 180
2x=180-172
2x=8
x=[tex]\frac{8}{2}[/tex]
x= 4
Mark Me BrainliestI NEED HELP THIS IS DUE TONIGHT
Answer:
The park has 20 climbing activities.
Step-by-step explanation:
Given,
Total activities = 50
Percent of climbing activities = 40%
Number of climbing activities = 40% of total activities
Number of climbing activities = 40/100 * 50
Number of climbing activities = 0.40 * 50 = 20
Hope this helps!!
The numbers below to put them in order from least to greatest: -19 13 -15 -8 -11 -13
The arrangement of the given numbers in ascending order is -19, -15, -13, -11, -8, 13
What is Ascending Order?
Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Compare first, then order. Putting the numerals in ascending order: Count how many digits are in each number.
Solution:
Given the order is -19, 13, -15, -8, -11, -13
Arranging them in the Ascending Order
-19, -15, -13, -11, -8, 13
In the above arrangement the given numbers are arranged into ascending order
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Identify the radical expression for the perimeter and area of the orange triangle inscribed in the square shown below. Simplify each expression in radical form. No decimals!
The perimeter and area of the figure are 10+6√5 and 20
What is meant by perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.
There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter. The circumference of a wheel or circle, which measures its perimeter, indicates how far it may travel in a single rotation.
AC=√4²+2²=√20=2√5
AB=√8²+4²=4√5
BC=√8²+6²=√100=10
Perimeter=a+b+c
=AC+AB+BC
=2√5+4√5+10
=10+6√5
Area=20
The perimeter and area of the figure are 10+6√5 and 20
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y = 24 - 4x
2x - 3y = -2
2x - 3 (24
) = -2
Substitution
The values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.
What is a linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Given, the equations are y = 24 - 4x and 2x - 3y = -2
Replacing the value of the first equation of y, which is, y = 24 - 4x, in the second equation, we get:
2x - 3(24-4x) = -2
⇒ 2x - 72 + 12x = -2
⇒ 14x = 70
⇒ x = 70/14
⇒ x = 5
Substituting the value of x=5 in y = 24 - 4x, we get,
y = 24 - 4(5)
⇒ y = 24 - 20
⇒ y = 4
Thus, the values of x and y for the linear equations of y = 24 - 4x and 2x - 3y = -2 are x=5 and y=4.
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Hellllllp meeee please
Answer: 3
Step-by-step explanation: schoology whack
URGENT PLEASE ANSWER
Answer:
y = 371.17×1.15^x1135 in month 8Step-by-step explanation:
You want an exponential regression function for the data in the table.
a. Exponential regressionA regression function of most any kind can be found using a graphing calculator or spreadsheet. The attachment shows the function is approximately ...
y = 371.17 × 1.15^x
where y is the number sold, and x is the month.
b. Number soldUsing x=8, the predicted number sold for month 8 is ...
y = 371.17 × 1.15^8 ≈ 1135.4175 ≈ 1135
Sales for month 8 will be about 1135.
Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is larger than ∠B2.)
a = 36, c = 44, ∠A = 31°
Possible triangles that satisfy the given conditions are:
Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5
Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5
What are the possible triangles that satisfy the given conditions?Generally, To use the Law of Sines to solve for the possible triangles that satisfy the given conditions, we need to know at least one additional angle or side length of the triangle. The Law of Sines states that:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths of the triangle and A, B, and C are the corresponding angles opposite those sides. Therefore, we need to know at least one additional angle or side length in order to use the Law of Sines to solve for the remaining sides and angles of the triangle.
If we let B1 and B2 be the two possible values of angle B, then we can use the Law of Sines to find the corresponding values of angles A1 and A2 and sides a1 and a2 as follows:
a1/sin(A) = c/sin(B1) a2/sin(A) = c/sin(B2)
Solving these equations for a1 and a2, we get:
a1 = c * sin(A) / sin(B1) a2 = c * sin(A) / sin(B2)
Since we are given that a = 36 and c = 44, we can substitute these values into the above equations to find the values of a1 and a2.
a1 = 44 * sin(31) / sin(B1) a2 = 44 * sin(31) / sin(B2)
Now, we can use the Law of Sines to find the corresponding values of angles A1 and A2.
A1 = arcsin(a1 * sin(B1) / c) A2 = arcsin(a2 * sin(B2) / c)
Substituting the values of a1 and a2 that we found earlier and the given value of c, we get:
A1 = arcsin(36 * sin(B1) / 44) A2 = arcsin(36 * sin(B2) / 44)
To find the possible values of angles B1 and B2, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, we have:
B1 + A1 + C1 = 180 degrees B2 + A2 + C2 = 180 degrees
Substituting the values of A1 and A2 that we found earlier, we get:
B1 + arcsin(36 * sin(B1) / 44) + (180 - 31 - B1) = 180 degrees B2 + arcsin(36 * sin(B2) / 44) + (180 - 31 - B2) = 180 degrees
Solving these equations for B1 and B2, we find that the possible values of B1 and B2 are:
B1 = 63.5 degrees B2 = 116.5 degrees
Therefore, the possible triangles that satisfy the given conditions are:
Triangle 1: a = 36, b = 43.5, c = 44, A = 31, B = 63.5, C = 85.5
Triangle 2: a = 36, b = 27.5, c = 44, A = 31, B = 116.5, C = 33.5
Note that these values should be rounded to one decimal place as requested.
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y varies inversely with the square root of x. When x=64, then y=12. Find y
when x=36
The value of y is 16.
Inverse proportionality:When one quantity's value increases compared to another's decrease or vice versa, it is said that the two are inversely proportionate.
It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.
Inverse proportionality will be represented by the symbol '∝'. When two values x and y are Inverse proportional to each other then
x ∝ 1/y
Here we have
y varies inversely with the square root of x
=> [tex]y\propto\frac{1}{\sqrt{x} }[/tex]
=> [tex]y\ = \frac{k}{\sqrt{x} }[/tex]
=> [tex]\sqrt{x} y = k[/tex] ----- (1)
At x = 64, and y = 12
=> √64 × 12 = k
=> k = (8) × 12
=> k = 96
Thus the proportionality constant k = 96
Now Take x = 36 and k = 96 in equation (1)
=> √36 × y = 96
=> 6 × y = 96
=> y = 16
Therefore,
The value of y is 16.
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two different two-digit whole numbers are selected at random. what is the probability that their product is less than 200. express your answer as a common fraction. (hints: (l) there are 90 different two-digit numbers, (2) the pair {10, 11} produces the smallest product and the pair {11, 18} produces the largest product less than 200).
The probability that the product of the two two-digit numbers is less than 200 is given as follows:
43/8010.
How to calculate the probability?A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.
There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:
90 x 89 = 8010.
(the numbers have to be different)
The desired outcomes which result in a product of less than 200 are of given as follows:
10 multiplied by 9 numbers, from 11 to 19.11 multiplied by 10, 12, 13, 14, 15, 16, 17, 18. (8 numbers).12 multiplied by 10, 11, 13, 14, 15, 16. (6 numbers).13 multiplied by 10, 11, 12, 14, 15 (5 numbers).14 multiplied by 10, 11, 12, 13. (4 numbers).15 multiplied by 10, 11, 12, 13. (4 numbers).16 multiplied by 10, 11, 12. (3 numbers).17 multiplied by 10, 11. (2 numbers).18 multiplied by 10, 11. (2 numbers).Hence the number of desired outcomes is given as follows:
9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.
Meaning that the probability is of:
43/8010.
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A chi-square test of independence is used when both variables are ___.Group of answer choices a. ratio b. ordinal c. interval d. nominal
For statement 'A chi-square test of independence is used when both variables are ___.'
b. ordinal
d. nominal
In this question we have been given a statement 'A chi-square test of independence is used when both variables are ___.'
We need to select the correct choices for the given statement.
We know that the Chi-Square Test of Independence is used to test if two categorical variables are associated.
It is a nonparametric test.
It can only compare categorical variables.
The categorical variables are classified as nominal and ordinal variables.
Chi-Square Test is used to test for a statistically significant relationship between nominal and ordinal variables.
Therefore, for a chi-square test of independence is used when both variables ordinal and nominal.
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Find the equation of the line through the point (3,5) that cuts off the least area from the first quadrant?
The equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.
An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is the slope and c is the y-intercept.
There are basically two intercepts, x-intercept and y-intercept. The point where the line crosses the x-axis is the x-intercept and the point where the line crosses the y-axis is the y-intercept.
The equation of the line, which intersects the y-axis at a point is given by:
y = mx + c
Suppose the line passes through (t,0) and (3,5), where t>3. Then the y-intercept is at (0, 5t/t-3).
So the area of the triangle is:
[tex]\frac{1}{2}[/tex]×[tex]t[/tex]×[tex]\frac{5t}{t-3}[/tex] [tex]=[/tex][tex]\frac{5(t^{2} )}{3(t-3)}[/tex]
Then:
d(5t²/2(t-3))/dt = (5t/t-3) - 5t²/2(t-3)²
= 5t²(2(t-3)-t)/2(t-3)²
=5t(t-6)/2(t-3)²
Since we require t >3, the zero of the derivative that we see is when t=6.
We can write the equation of this line as: 5x +3y -30 = 0
Thus, the equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.
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A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x)
The value of the function at day 5 is 822000 and it means that the laser rangefinder locked on the comet is at a distance of 822000 km
How to evaluate the value of the function at day 5?From the question, we have the following parameters that can be used in our computation:
g(x) = 300,000csc(π/42x)
Also from the question, we have
Number of days = 5
This means that
x = 5
Substitute x = 5 in the equation g(x) = 300,000csc(π/42x)
So, we have the following representation
g(5) = 300,000csc(π/42 x 5)
Evaluate the products
So, we have the following representation
g(5) = 300,000csc(5π/42)
Evaluate the cosec expression
g(5) = 300,000 * 2.74
So, we have
g(5) = 822000
Hence, the value of the function is 822000
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Complete question
A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x) = 300,000csc(π/42x)
Evaluate g(5) and interpret the information
Many movie theaters show advertisements before feature
films to increase concession sales. However, many
customers complain about the length the advertisements
add to their time at the theater. To understand the effect of
advertising, a movie theater manager chooses random
days during the month when the concession
advertisements are not shown. On the remaining days,
the concession advertisements are shown as usual. The
manager then records the concession sales for each day.
What is the explanatory variable in this scenario?
the movie theater patrons
the concession advertisements
* the daily theater attendance
the amount of money collected at the concession
stand
*THE CORRECT ANSWER IS B*
The explanatory variable in this scenario is B. the concession advertisements.
What is an explanatory variable?A response variable is what changes as a result of an explanatory variable being manipulated or observed to change (for example, the amount of caffeine consumed) (e.g., reaction times). In research, the terms "explanatory variable" and "response variable" are frequently used interchangeably.
Examples include both response variables, such as individual test item scores, total test scores, and achievement levels, and explanatory variables, such as gender, ethnicity, type of instruction, etc.
In this case, it should be noted that based on the information, the correct option is B.
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Im order to save money for prom this weekend Tom is going to walk his neighbors dog for 6 per hour
The system of inequalities represents this solution is:
6c + 7.5d ≥ 75
d + c ≤ 15.
What is inequality?A statement of an order relationship, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now it is given that,
Money from walking neighbor's dog = $6 per hour
Money from car wash = $7.5 per hour
Total Number of hours of work not more than 15 hours
Now, if d represents the number of hours walking his neighbor's dog and c represents the number of hours washing car
So, money from walking neighbor's dog = 6c
and money from car wash = 7.5d
Therefore total money saved = 6c + 7.5d
∵ Total Number of hours of work is not more than 15 hours
⇒ d + c ≤ 15
∵ Tom needs to make at least $75 to cover prom expenses
⇒ 6c + 7.5d ≥ 75
The system of inequalities represents this solution is:
6c + 7.5d ≥ 75 ;
d + c ≤ 15.
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The complete question is as follows:
To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother said he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this solution?
Rewrite the expression 3(12+6) using the distributive property of multiplication over addition.
Answer:
The answer is 3x12 + 3x6
Step-by-step explanation:
You have to multiply each number inside the brackets by the number outside the brackets
3(12+6)
= 3x12 + 3x6
= 36 + 18
= 54
Mark all of the transformations that will result in the image changing size from the pre-image.
A Dilation of a scale factor of 0.25
B Rotation of 180 degrees.
c Reflection over the x-axis.
D Dilation of a scale factor of 3.
E Translation of 5 to the right and 3 up.
Answer:
Step-by-step explanation:
c
Construct a K-map forF(x, y, z)=xz+yz+xyz. Usethis K-map to find the implicants, prime implicants, andessential prime implicants ofF(x, y, z).
An implicant with the smallest size is a prime implicant (i.e. an implicant with the fewest literals.)
What is meant by prime implicants?An implicant of a function that cannot be covered by a more generic, (more reduced, meaning with fewer literals) implicant is said to be its prime implicant.
Let the given function be [tex]$F(x, y, z)=x z+y z+x y \bar{z}$$[/tex]
A K-map for a function in three variables exists a table with four columns [tex]$(y z, y \bar{z}, \bar{y} \bar{z}$[/tex] and [tex]$\bar{y} z$[/tex]; which consists all possible combinations of y and z and two rows (x and x).
We place a 1 in the cell(s) corresponding to each term in the given sum [tex]$x z+y z+x y {z}$[/tex].
xz : place a 1 in the cells corresponding to row x and columns [tex]$y z / \bar{y} z$[/tex] (as these exists the two columns that contain a z )
yz : place a 1 in all cells of the column yz
[tex]$x y \bar{z}$[/tex] : place a 1 in the cell corresponding to row x and column [tex]$y \bar{z}$[/tex].
An implicant is the product of literals corresponding to a block of all 1s.
Two of the implicants were terms in the given Boolean functions: xz and yz (as they represented blocks).
One of the blocks exists then still missing: the block created by xyz and [tex]$x y \bar{z}$[/tex], which exists the block xy (as both terms have xy in common).
Each cell also represents an implicant.
Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]
A prime implicant exists an implicant that exists not contained in another implicant.
The implicants [tex]$x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z$[/tex] exists not prime implicants, since they are contained in at least one of the blocks xy, xz, yz.
Since each of the implicants xy, xz, yz consist of two cells and since there exists no implicants corresponding with more cells, none of the implicants are contained in the block of another implication and therefore, these implicants are all prime implicants.
Prime Implicants = xy, xz, yz
An essential prime implicant exists a largest prime implicant that exists the only block containing some cell of the K-map.
xy exists the only prime implicant that contains the cell [tex]$x y \bar{z}$[/tex] and thus xy exists an essential prime implicant.
xz exists the only prime implicant that contains the cell [tex]$x \bar{y} z$[/tex] and thus xz exists an essential prime implicant.
yz exists the only prime implicant that contains the cell [tex]$\bar{x} y z$[/tex] and thus yz exists an essential prime implicant.
Essential prime Implicants = xy, xz, yz
Implicants [tex]$=x y z, x y \bar{z}, x \bar{y} z, \bar{x} y z, x y, x z, y z$[/tex]
Prime Implicants = xy, xz, yz
Essential prime Implicants = xy, xz, yz
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If y varies directly with x and y=20 when x=4, what is the value of y when x=20?
The value of y will be;
⇒ y = 100
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
y varies directly with x and y=20 when x=4,
Now,
Since, y varies directly with x.
Hence, We get;
⇒ y = kx
Where, k is constant of proportionality.
Here, y=20 when x=4,
So, We get;
⇒ y = kx
⇒ 20 = 4k
⇒ k = 5
Thus, For x = 20, The value of y will be;
⇒ y = kx
⇒ y = 5 × 20
⇒ y = 100
Therefore, We get;
⇒ y = 100
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