Answer:
B
Step-by-step explanation:
49x^2=9
solve for x
x^2= 9/49
x=± [tex]\sqrt{9/49\\}[/tex]
which is x = ±3/7 (B)
Answer: b x=1/9 and x=-1/9
Step-by-step explanation:
what is true for f (x) = 4 times 2x
Answer:
f(x) = 8x
Explanation:
4 x 2 =8
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
Using the digits 2 through 8, find the number of different 5-digit numbers such that, digits can be used more than once.
Answer:
7 digits can be used for each position
There are a total of 5 positions
N = 7^5 = 16,807 numbers
You have 7 choices for the first position, second position, etc.
rank the three fractions from smallest to largest? and why
2/7, 4/14, 8/11
Answer:
2/7 = 4/14 so from smallest to largest the fractions are:
2/7 4/14 and 8/11
Step-by-step explanation:
Joshua asked each of his friends how many coins they donated to the school fundraiser. The range of this set is 110 and the lowest number of coins is 98. what is the greatest number of coins donated
Answer:
208
Step-by-step explanation:
use the formula x-98=110 since range is the highest number of the group subtracted by the lowest.
Carlos has an aquarium which is 45 cm long, 32 cm wide, and 35 cm high. How much water can the aquarium hold?
Answer:
volume =l×b×h
45cm×32cm×35cm=48,960cm³
A strawberry farmer in Poteet knows that 1/8 of his strawberries are typically not fit to sell at the market (either because they went bad or are too unusually shaped). The farmer takes a random sample of 156 strawberries to inspect for the upcoming farmer's market and finds that 24 are unfit to sell. If he were to go back and pick 1000 more strawberries to inspect for the market, how would the standard deviation of the sample proportion be affected
Answer:
It would be smaller.
Step-by-step explanation:
Given that :
The number of the strawberries that are unfit for sell, x = 24
The total number of the strawberries to inspect, n = 156
Total number of the strawberries to be picked = 1000 strawberries
Therefore,
[tex]$\widehat p =\frac{x}{n}$[/tex]
[tex]$=\frac{24}{156}$[/tex]
= 0.1538
[tex]$\widehat p =\frac{x}{n}$[/tex]
[tex]$=\frac{24}{1000}$[/tex]
= 0.024
Therefore, the standard deviation of the sample proportion would be smaller.
Find x. Simplify completely.
16
25
X =[?]
Answer:
20
Step-by-step explanation:
a)x^2+16^2=a^2
b)x^2+25^2=b^2
c)a^2+b^2=(16+25)^2
a+b)2x^2+25^2+16^2=41^2=a^2+b^2
2x^2=800
x=20
The equation for the pH of a substance is pH = -log[H], where Ht iS the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration
of hydrogen ions between the two solutions?
Answer:
The difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.
Step-by-step explanation:
The pH is given by:
[tex] pH = -log[H^{+}] [/tex]
Where:
[tex] [H^{+}][/tex]: is the concentration of hydrogen ions.
For the basic solution (pH = 11.2), the concentration of H⁺ is given by:
[tex] [H^{+}]_{b} = 10^{-pH} = 10^{-11.2} = 6.31 \cdot 10^{-12} [/tex]
And, for the acidic solution (pH = 2.4) we have:
[tex] [H^{+}]_{a} = 10^{-pH} = 10^{-2.4} = 3.98 \cdot 10^{-3} [/tex]
Hence, the difference in the concentration of H⁺ between the two solutions is:
[tex] \Delta H^{+} = [H^{+}]_{a} - [H^{+}]_{b} = 3.98 \cdot 10^{-3} - 6.31\cdot 10^{-12} = 3.98 \cdot 10^{-3} [/tex]
Therefore, the difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.
I hope it helps you!
Answer:
B. 4.0 x [tex]10^{-3}[/tex]
Step-by-step explanation:
EDG2021
integrate G(x,y,z)=yz over the surface of x+y+z=1 in the first octant.
Parameterize the surface (I'll call it S) by
r(u, v) = (1 - u) (1 - v) i + u (1 - v) j + v k
with 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.
Take the normal vector to this surface to be
n = ∂r/∂u × ∂r/∂v = ((v - 1) i + (1 - v) j) × ((u - 1) i - u j + k) = (1 - v) (i + j + k)
with magnitude
||n|| = √3 (1 - v)
Then in the integral, we have
[tex]\displaystyle\iint_SG(x,y,z)\,\mathrm ds = \int_0^1\int_0^1 G((1-u)(1-v),u(1-v),v) \|\mathbf n\| \,\mathrm du\,\mathrm dv \\\\= \sqrt3 \int_0^1\int_0^1uv(1-v)^2\,\mathrm du\,\mathrm dv \\\\= \boxed{\frac1{8\sqrt3}}[/tex]
Alternatively, if you're not familiar with parameterizing surfaces, you can use the "projection" formula:
[tex]\displaystyle\iint_S G(x,y,z)\,\mathrm ds = \int_{S_{xy}}G(x,y,z)\sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}\,\mathrm dx\,\mathrm dy[/tex]
where I write [tex]S_{xy}[/tex] to mean the projection of the surface onto the (x, y)-plane, and z = f(x, y). We would then use
x + y + z = 1 ==> z = f(x, y) = 1 - x - y
and [tex]S_{xy}[/tex] is the triangle,
{(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}
Then the integral becomes
[tex]\displaystyle\int_0^1\int_0^{1-x}y(1-x-y)\sqrt{1+(-1)^2+(-1)^2}\,\mathrm dy\,\mathrm dx \\\\= \sqrt3\int_0^1\int_0^{1-x} y(1-x-y)\,\mathrm dy\,\mathrm dx \\\\= \frac{\sqrt3}{24} \\\\= \boxed{\frac1{8\sqrt3}}[/tex]
Why can you use cross products to solve the proportion StartFraction 18 over 5 EndFraction = StartFraction x over 100 EndFraction for x?
Answer:
45
Step-by-step explanation:
PLEASE HELPPP ASAP!!! I tried all sorts of equations but no correct answer! Not sure how to approach this problem.
Answer:
[tex]44[/tex]
Step-by-step explanation:
The dimensions of the garden is 12 by 8. If we have a walkway that surrounds the garden, the dimensions of the walkway is 2. Since it surrounds the rectangle all sides add 2 to each of the dimensions so now the dimensions of the garden and walkway is 14×10.
The area of the garden is 96 square ft.
The area of the garden and walkway is 140 so let subtract the area of the garden from the total area of both the garden and walkway.
[tex]140 - 96 = 44[/tex]
The area is 44.
Answer:
120 square feet
Step-by-step explanation:
(8+2*2)
(18+2*2) - 8*18 = 120 square feet.
Determine the value of the missing letters in the sum of numbers
below:
ab1
+ ba
abb
49x
Answer:
a=2, b=3,x=6
Step-by-step explanation:
We are given that
We have to find the value of the missing letters in the sum of numbers.
From given sum
1+a+b=x ....(1)
b+b+b=9 .....(2)
a+a=4 ......(3)
From equation (2) we get
[tex]3b=9[/tex]
[tex]\implies b=3[/tex]
From equation (3) we get
[tex]2a=4[/tex]
[tex]a=4/2[/tex]
[tex]a=2[/tex]
Now, substitute the values in equation (1) we get
[tex]1+2+3=x[/tex]
[tex]x=6[/tex]
Therefore,
231+32+233=496
Statesville's population in 2010 was about 24,500, and was growing by about 1% each year. continues, what will Statesville's population be in 2019? [Round to the nearest person.]
Answer:
26,795 people
Step-by-step explanation:
P(x) = 24,500 × (1 + 0.01)^(2019-2010)
= 24,500 × (1.01)^9
= 24,500 × 1.0937
= 26,795 people
The required population of Statesville in the year 2019 will be 26,795.
Statesville's population in 2010 was about 24,500, growing by about 1% each year. Statesville's population be in 2019 to be determined.
The function which is in format f(x) = a^x where, a is constant and x is variable, the domain of this exponential function lies ( -∞, ∞ ).
Let Statesville's population in 2019 = x
Statesville's population in 2010 = 24500
Population growing by about 1% = 1/100
= 0.01
Difference in year n = 2019 - 2010
n = 9
Population in 2019,
x = 24500 * ( 1 + 0.01 )^9
x = 24500 * ( 1.01 )^9
x = 26, 795.295
To the nearest people x = 26,759
the population of Statesville in the year 2019 = 26,759
Thus, the required population of Statesville in the year 2019 will be 26,795.
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Let F(x) = x^2 – 15 and
G(x)= 4 - x
Find (F/G)(–7) =
Answer:
[tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
F(x) = x² - 15
G(x) = 4 - x
Step 2: Find
Substitute in functions: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(x) = \frac{x^2 - 15}{4 - x}[/tex]Step 3: Evaluate
Substitute in x [Function (F/G)(x)]: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{(-7)^2 - 15}{4 - (-7)}[/tex]Exponents: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{49 - 15}{4 - (-7)}[/tex]Subtract: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}[/tex]What is the sum of the first 7 terms of the geometric series:
Answer:
-15.875
Step-by-step explanation:
First, we can sum up the first 5 terms.
-8 + (-4) = -12
-12 + (-2) = -14
-14 + (-1) = -15
-15 + (-1/2) = -15.5
Next, we can find a pattern in the data. We can tell that the next number is one half of the current number. For example, -4 is one half of -8. To find the next number, we simply multiply our current number by one half. Thus, the sixth number is -1/4 and the seventh is -1/8. Adding these to our current total, we have
-15.5 - 1/4 = -15.75
-15.5 - 1/8 = -15.875 as our answer
find the HCF by prime factorization method 60 and 75
HCF=15
Hope it helps you...
Please help me i will give you brainlest
Answer:
x = 14/3
Step-by-step explanation:
9.
The given equation is:
(x-2)+(x-3)+(x-9)=0
After opening the brackets,
x-2+x-3+x-9=0
3x+(-2-3-9) = 0
3x-14=0
x = 14/3
So, the value of x is equal to 14/3.
Analyze the figure below and complete the instructions that follow.
Answer:
C. 468 mm²
Step-by-step explanation:
Surface area of the composite solid = 2(LW + LH + WH)
Length (L) = 12 mm
Width (W) = 6 mm
Height (H) = 2 + 7 = 9 mm
Plug in the values into the formula
Surface area = 2(12*6 + 12*9 + 6*9)
Surface area = 2(72 + 108 + 54)
Surface area = 2(234)
= 468 mm²
Help me on this please
Answer:
x = 3.5
Step-by-step explanation:
Triangle to the right:
4^2 + x^2 = 8^2
16 + x^2 = 64
y^2 = 48
Triangle to the left:
x^2 + 6^2 = 48
x^2 + 36 = 48
x^2 = 12
x = sqrt(12)
x = 3.5
√(9+ √32)
Please simplify
Answer:
3.82
Step-by-step explanation:
[tex]\sqrt{(9+\sqrt{32}) }[/tex] Do not confirm the answer unless your equation looks like that?
[tex]\sqrt{(9+\sqrt{32}) }[/tex] Start by the [tex]\sqrt{32}[/tex]
[tex]\sqrt{(9+5.65) }[/tex] Now add (9 + 5.65)
[tex]\sqrt{14.65}[/tex] Finally Simplify
[tex]3.82[/tex] Final answer
In order for the parallelogram to be a
rhombus, x = [?].
(5x + 25)
(12x + 11)
A parallelogram is also a rhombus if the diagonal is a bisector of an angle enclosed by the two adjacent sides of a parallelogram.
In our case it means,
[tex]5x+25=12x+11[/tex]
[tex]7x=14\implies x=\boxed{2}[/tex]
Hope this helps.
In order for the parallelogram to be a rhombus, ,For the parallelogram to be a rhombus, x must be equal to 2.
To determine the value of x that would make the parallelogram a rhombus, we need to compare the lengths of its opposite sides. In a rhombus, all four sides are equal in length. So, we can equate the lengths of the opposite sides of the parallelogram and solve for x.
Given that one side has a length of (5x + 25) and the opposite side has a length of (12x + 11), we can set up the following equation: 5x + 25 = 12x + 11
To solve for x, we can start by isolating the x term on one side of the equation. We can do this by subtracting 5x from both sides: 25 = 12x - 5x + 11 Simplifying the equation further: 25 = 7x + 11 Next, we can isolate the x term by subtracting 11 from both sides: 25 - 11 = 7x 14 = 7x Finally, we can solve for x by dividing both sides by 7: 14/7 = x x = 2 Therefore, for the parallelogram to be a rhombus, x must be equal to 2.
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Circle Theorems 1! need help
Answer:
45°
Step-by-step explanation:
<lmk=90°
angles in a triangle add up to 180
45+90+<o=180
<o=180-135
<o=45
Answer:
∠ O = 45°
Step-by-step explanation:
The angle between the tangent and the radius at the point of contact is 90°
The sum of the 3 angles in Δ OML is 180° , then
∠ O = 180° - (90 + 45)° = 180° - 135° = 45°
The function f(x) is shown in this graph. The function g(x) = -7x - 1. Compare the slopes.
Answer:
D
Step-by-step explanation:
Slope of the first line = (1-3)/1 = -2
An amusement park offers 2 options on tickets into the park. People can either buy 5 admission tickets for $130 or buy 1 admission ticket for $30. How much money will a group of 5 people save by buying 5 admission tickets for $130?
Answer:
You could save $20
Step-by-step explanation:
For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130
Answer:
20 dollars
Step-by-step explanation:
for the first deal is 5 for $130
and the second is for $30
$30 times 5 (the number of people) = $150
$150-$130= is 20
answer: $20
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The firm’s three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $15 for David, and $18 for Sarah.Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Answer:
a) Minimize Z =30 X1 +25 X2+18 X3
subject to following constraints
[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]
b) Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.
c) As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.
Step-by-step explanation:
Step 1:-
a)
Let's take
X1 to be the number of hours assigned to Lisa
X2 to be the number of hours assigned to David
X3 to be the number of hours assigned to Sarah.
The objective function is to attenuate the entire cost of the project by deciding an optimum number of hours for every person. the target function is given by -
Minimize Z =30 X1 +25 X2+18 X3
subject to following constraints
[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]
Constraints and explanation:
1. Lisa must be assigned a minimum of 40% of the entire number of hours assigned to the 2 senior designers.
2. Sarah must be assigned a minimum of 15% of the entire project time.
3. The corporate estimates that 150 hours are going to be required to finish the project.
4. The number of hours assigned to Sarah must not exceed 25% of the entire number of hours assigned to the 2 senior designers.
5. Lisa features a maximum of fifty hours available to figure on this project.
6. Non-negative condition.
Step 2:-
b)
From the above equations, we get
The number of hours assigned to Lisa is 48 hours
The number of hours assigned to David 72 hours
The number of hours assigned to Sarah 30 hours.
Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.
Step 3:-
c)
As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.
The ratio of the number of cherry tomatoes in a tossed salad to people served is 7:15. If Waldo wants to serve 105 people, how many cherry tomatoes will Waldo use
Select the correct answer. Simplify. (3x^2y^3/z^3)^3 A. B. C. D.
Answer:
options aren't given but the correct answer will be [tex]\frac{27x^6y^9}{z^9}[/tex]
Step-by-step explanation:
The simplified form of (3x²y³/z³)³ is 27x⁶y⁹/z⁹.
To simplify the expression (3x²y³/z³)³, we apply the rules of exponents. When we raise a power to another power, we multiply the exponents.
First, let's apply the exponent of 3 to each term inside the parentheses:
(3x²y³/z³)³ = 3³ × (x²)³ × (y³)³ / (z³)³
Simplifying further:
= 27 × x⁶ × y⁹ / z⁹
Therefore, the simplified form of (3x²y³/z³)³ is 27x⁶y⁹/z⁹.
This means that each term inside the parentheses is raised to the power of 3, resulting in the expression 27x⁶y⁹/z⁹.
The final expression represents the cube of the original expression, where each term is cubed individually. The exponents are multiplied by 3 to reflect this operation.
In summary, the simplified form is 27x⁶y⁹/z⁹.
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A factory produces 80 % round and 20 % square buttons. Suppose that 10 % of theround buttons and 50 % of the square buttons are red. What is the probability that arandomly selected red button is square?
Answer:
5/9
Step-by-step explanation:
Let the total number of buttons is x.
Round buttons = 80% of x = 0.8xSquare buttons = 0.2xNumber of red buttons:
0.1*0.8x + 0.5*0.2x = 0.08x + 0.1x = 0.18xNumber of red square buttons is 0.1x
Required probability:
P = 0.1x/0.18x = 10/18 = 5/9i got some summer h.w it doesn't have a answer but like it asks for me to Create a table of x and y values that represents a proportional relationship. and i dont know how cause it wont let me draw a graph so i have to write something down apparently any help pls?
Answer:
So for example a graph in typed in word format could look like
Time Girls Boys
1 3 5
2 4 6
3 5 7
4 6 8
5 7 9
Not saying that this graph would be sufficient value wise for the answer, but this is how I would tackle it if I wasn't given the option to draw a graph.
