The scale factor from B to A is 5/8. Since the scale-up and scale-down of A and B are reciprocal to each other. I.e, scaling of geometry can be reversed by the reciprocal of its scale factor.
What is meant by a scale factor and how is it calculated?Scale factor: A number that is multiplied by the components of an object to create an enlargement or reduction of the object.Scale factor = new length/original length There are two kinds of scaling. They are scale-up and scale-down.Scale-up is nothing but enlarging the shape and scale-down means reducing the shape.The scaling of an object or shape is reversed by finding the reciprocal of its scale factor. If the scale factor is greater than 1 then it goes under enlargement and if it is less than 1, then it goes under reduction.Calculation:The scale factor for the given shape to transform from A to B is 8/5.
So, the original shape is A and it is scaled up by the factor 8/5 and named B.
(Scaled up since scale factor (8/5 = 1.6) > 1)
So, the scaling from B to A is the reverse process of scale-up. That means scale-down. For this, the scale factor is reduced by taking its reciprocal. So, that the shape gets reversed.
The scale factor for scaling down from B to A is 1/(8/5) ⇒ 5/8.
Therefore, the scale factor from B to A is 5/8.
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what is the conditional probability that a randomly-generated 4-bit string contains two consecutive 1s, given that the first bit of the string is a 1?
The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .
total length of four-bit strings = 16
Let S represent the collection of all four-bit bit strings.
Let A represent the occurrence of a randomly generated string beginning with 1.
Let B represent the scenario where a string created at random contains two consecutive 0s.
S has 8 strings that begin with the letter "1."
P( A ) = 8 / 16 = 1 / 2
Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100
P(A ∩ B) = 3 / 16
Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,
3/16 / 1/2
= 3 / 8
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Divide. Check your solutions by multiplying.
1. 409÷5
Answer:
Step-by-step explanation:
409/5 is 1/8. then 81.8 and then check by multiplying 81.8 by 5 and that equals 409.
Need help
What criteria are necessary to prove that two triangles are congruent to one another?
Answer:
SSS, SAS, ASA, AAS
Step-by-step explanation:
s = sides
a = angle
Help me answer this question for a 10 on my homework
Answer:
1. 4
2. rise = 2; run = 1; slope = 2
3. y = 2x + 4
Step-by-step explanation:
1. Look at the graph. On the y-axis, the line passes through 4. The line crosses the y-axis at 4, so 4 is the y-intercept, and b = 4 in the equation y = mx + b.
2. Choose any two points on the line. I choose the y-intercept, (0, 4) and point (-1, 2).
slope = rise/run
We need to go from point (-1, 2) to point (0, 4) by only moving vertically and horizontally. Start at (-1, 2). Go up 2 units. That is a ris of 2. Now go right 1 unit to arrive at point (0, 4). that is a run of 1.
slope = rise/run = 2
3. We have b = 4, and m = 2.
y = mx + b
y = 2x + 4
The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 6:19. There are 57 gallons of gasoline. How many ounces of oil are there?
2 ounces
18 ounces
24 ounces
180.5 ounces
According to the specified ratio , we obtain The gasoline contains 18 ounces of oil.
What's does ratio mean?The number, volume, or size difference between two or more items is known as their proportion.We got the word "ratio" directly from the Latin word, which is also called "suitable ratio." The mathematics and English ratios were derived from the Latin ratio, which had multiple meanings, ranging from "reason" to "calculation" to "proportion."Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.The fuel for a chain saw is a mix of oil and gasoline.
The ratio of ounces of oil to gallons of gasoline is 6:19.
So oil : gas = 6:19
There are 57 gallons of gasoline
⇒ oil : gas = 6:19
Let there are x gallons of ounces of oil
So x : 57 = 6:19
Convert ratio to fraction
⇒ x/57 = 6/19
Multiply both sides by 57
⇒ x = (6/19)57
⇒ x = 18
Hence, there are 18 ounces of oil in the fuel.
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One group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house. At which house will they first meet?
The house that they will first meet if a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house is the 24th house.
How to calculate the multiple?The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory. Since the result of dividing an integer by zero is undefinable, this definition only applies if both a and b are not equal to zero.
Before fractions can be added, subtracted, or compared, the "lowest common denominator" can be employed.
From the information, a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house.
It should be noted that this will be illustrated through tye lowest common multiple.
Multiples of 6 = 6, 12, 18, 24
Multiples of 8 = 8, 16, 24
Therefore, they'll meet at the 24th house.
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Sandy uses three and one half pounds of clay to make 7 small vases. Use a proportion to find how many pounds of clay she will use to make 21 small vases.
7 and one fourth pounds
8 and one half pounds
10 and one half pounds
14 and one fourth pounds
The number of pounds of clay used to make 21 small vases is 10 and one half pounds.
How to find the number of pounds of clay used to make vases?Sandy uses three and one half pounds of clay to make 7 small vases. Using proportion, the number of pounds of clay that she can use to make 21 small vases can be calculated as follows;
Therefore,
7 small vases = 3 1 / 2 pounds of clay(7 / 2)
21 small vases = ?
cross multiply
pounds of clay used to make 21 small vases = 7 / 2 × 21 ÷ 7
pounds of clay used to make 21 small vases = 147 / 2 ÷ 7
pounds of clay used to make 21 small vases = 147 / 2 × 1 / 7
pounds of clay used to make 21 small vases = 21 / 2
Therefore,
pounds of clay used to make 21 small vases = 10 1 / 2
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Steven is a waiter. He earns $3.45 an hour plus 20% tips. One day he worked 7 hours and served meals costing $497 what were his earring? Round you answer to the nearest cent.
50 POINTS!!! Which graph represents this system? y = 3. x + y = 4. Which graph represents this system? y = 3. x + y = 4. On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (3, 7). On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (2, 6). On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (4, 0). On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).
For a system with equations y = f(x) and y = g(x), the graph of the system will be just a coordinate plane with the two functions graphed on it.
What is functions graphed?
What Does Graphing Functions Mean? Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) represents the function. As an illustration, the graph below depicts the linear function f(x) = -x+ 2.
From this, we can see that the correct option is the first one:
"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."
Also a graph of the system can be seen at the end of this answer.
Here our system is:
y = 3
x + y = 4
The first one is a horizontal line at y = 3.
The second can be rewritten as:
y = -x + 4
So this is a line with a negative slope, that passes through the points (0, 4) (when you evaluate in x = 0, you get y = 4) and (4, 0) (when you evaluate in x = 4, you get y = 0)
Then the correct option is the first one:
"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."
The graph can be seen below
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Find the values of x and z !!
The value of x and z are [tex]4^\circ, 96^\circ[/tex].
Now from the picture I can say that, [tex]\angleAOB[/tex][tex]\angle AOB[/tex] and [tex]\angleCOD[/tex][tex]\angle COD[/tex] are opposite angles.
We know the measure of the triangle are equal in Pair.
So we have got the equation as -
[tex]10x+44=13x+32[/tex]
⇒[tex]13x-10x=44-32[/tex]
⇒3x=12
⇒x=4.
We have got that the measure of [tex]\angle AOB, \angle COD[/tex] are both [tex]84^\circ[/tex].
Now angles around a point add to [tex]360^\circ[/tex].
So, [tex]\angle AOD[/tex] and [tex]\angle BOC[/tex] are equal since they are pairwaite wisw.
Now, [tex]z+z= 360^\circ - (84^\circ+84^\circ)[/tex]
⇒[tex]2z=192^\circ[/tex]
⇒ [tex]z=96^\circ[/tex],
Hence we have got the value of x and z i.e. 4 and 96.
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in how many ways can four people line up in a straight line if the youngest person cannot be first in line?
Total number of ways four people line up in the straight line with the given condition is equal to 18 ways.
As given in the question,
Total number of people = 4
Given condition :
First position can not occupied by youngest person:
First position occupied in 3 ways
Second position occupied in 3 ways
Third position occupied in 2 ways
fourth position occupied in 1 ways
Total number of ways = 3 × 3 × 2 × 1
= 18 ways
Therefore, the number of ways four people stand in straight line is equal to 18 ways.
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4. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).
The proof that AB = CD in the concentric circles is shown below
How to prove the equation AB = CDFrom the question, we have the following parameters that can be used in our computation:
The concentric circles
This means that the circles have the same center
From the circles, we have the following congruent lines
AC = BD
Subtract BC from both sides of the equation
So, we have the following representation
AC - BC = BD - BC
Evaluate the difference
This gives
AB = CD
Hence, it is true that AB = CD
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Answer:
Hope it will help you...
A cylindrical dog feeder is 18 inches tall and has a diameter of 8 inches if the feeder is currently half full, how much more food can be poured into the feeder? Use 22/7 for pie and round to the nearest cubic inch.
453 cubic units of food is poured to the cylindrical dog feeder of 18 inches tall and has a diameter of 8 inches.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the cylindrical dog feeder is 18 inches tall and has a diameter of 8 inches
height is 18 inches
Diameter=8 inches
Radius =4 inches
The feeder is currently half full, how much more food can be poured into the feeder.
We know that volume of a cylinder is V=πr²h
Substitute the values of r and h in the given formula.
V=22/7(4)²×18
=22×16×18/7
=6336/7
=905.142.
As the feeder is currently half full, so let divide the volume by 2.
905.142/2
=452.5
=453
Hence, 453 cubic units more food is need or poured into the feeder.
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Noah is baking cookies. the recipe he is using makes 48 cookies and uses 1/4 cup of sugar. How much sugar will Noah need to make 72 cookies?
Answer: Approx. 0.375 cups of sugar
Step-by-step explanation:
1/4=0.25
0.25 cups of sugar per 48 cookies = 0.25/48= (about) 0.00520833333 per cookie
0.00520833333 cups of sugar x 72 cookes= 0.375 cups of sugar for 72 cookies
The cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet. It costs $3,000 to paint a room with a surface area of 1,500 square feet. Determine an equation that gives the relationship between c and a.
The equation that gives the relationship between cost (c) and area (a) is c = 2a
How to determine an equation that gives the relationship between cost and area?A variation is a relation between a set of values of one variable and a set of values of other variables
Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet
We can write:
c α a
c = ka
where k is the constant of proportionality
since c = $3,000 and a = 1500
c = ka
3000 = 1500k
k = 3000/1500
k = 2
Thus, the equation of the relationship is c = 2a
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Simplify the expression 10^log5
Answer:
5
Step-by-step explanation:
The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."
Using this definition, we can simplify the expression "10^log5" as follows:
10^log5 = 10^y
Where "y" is the exponent to which the base "10" must be raised to produce the result "5."
To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:
log(10^y) = y
Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:
log(5) = y
Solving for "y," we find that "y = log(5)."
Therefore, the expression "10^log5" can be simplified to:
10^log(5) = 10^(log(5)) = 5
So the simplified result is 5.
according to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (n) and a 45% chance of experiencing decreased sexual drive (d). the information also states that there is a 14% chance of experiencing both side effects. what is the probability of experiencing only nausea?
The probability of experiencing only nausea is 0.06.
Using Venn Probabilities, it is found that there is a 0.45 = 45% probability of experiencing neither of the side effects.
What is a Venn probability?
In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
P(N∪D) = P(N) + P(D) - P(N∩D)
In this problem, the probabilities given are:
P(N)= 0.2 , P(D)= 0.45 , P(N∩D) = 0.14
The "at least one" probability is:
P(N∪D) = 0.20 + 0.45 - 0.14 = 0.51
Hence, the "neither" probability is:
1 - P(N∩D) = 1 - 0.51 = 0.49
The probability of experiencing only nausea = P(nausea) - P(both side effects)
=0.20 - 0.14
=0.06
0.49 = 49% probability of experiencing neither of the side effects.
The probability of experiencing only nausea is 0.06.
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7. Olivia purchases gifts for her mom and
grandma
for Mother's Day. The first is a pair of
sunglasses for $16.35 and the second is a
bracelet. Her total is $39.75. How much did she
spend on the bracelet?
Answer: $23.40
Step-by-step explanation:
To find out how much Olivia spent on the bracelet, we need to subtract the cost of the sunglasses from the total amount spent. In this case, that would be $39.75 - $16.35 = $<<39.75-16.35=23.40>>23.40. Therefore, Olivia spent $23.40 on the bracelet.
Write a paragraph that explains how you solved the equation 4(t + 25) = 4(t + 50) - 4(0.15t). You may include equations as part of your explanation, but be sure to use correct math terminology and write in complete sentences.
The equation 4(t + 25) = 4(t + 50) - 4(0.15t) can be solved as explained below to determine the value of t, which is t = 166.67.
How to Solve an Equation?If we are given the equation, 4(t + 25) = 4(t + 50) - 4(0.15t), to find the value of the variable t, follow the steps explained below.
4(t + 25) = 4(t + 50) - 4(0.15t) [given]
Open the parentheses by applying the distributive property:
4t + 100 = 4t + 200 - 0.6t
Combine like terms:
4t + 100 = 3.4t + 200
4t - 3.4t = -100 + 200
0.6t = 100
Divide both sides by 0.6
0.6t/0.6 = 100/0.6
t = 166.67
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Consider the line -8x -6y = -4.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Slope of the line is .[tex]\frac{-4}{3}[/tex]
Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]
What is the slope of a line?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. As opposed to the net change in the x coordinate, the net change in the y coordinate is y.
y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
A line's slope is a measurement of how steep it is or the direction it is going in relation to a coordinate system.
where m is the slope and m = y/x
Take notice that tanФ = y/x.
This tanФ is often referred to as the line's slope.
Calculation:The given equation is of the form [tex]ax+by=c[/tex]
On comparing we can say that a is -8 and b is -6
So using the slope formula [tex]\frac{-A}{B}[/tex] we get slope as [tex]\frac{4}{-3}[/tex]
The perpendicular line slope can be found out by equation [tex]m1.m2=-1[/tex]
Therefore substituting slope from the above as m1 we get m2 = [tex]\frac{3}{4}[/tex]
Slope of the line is .[tex]\frac{-4}{3}[/tex]
Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]
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A chemist is investigating a new reaction to synthesize barite crystals. She finds that eight grams are synthesized every five minutes. If there are 111 grams of barite after an hour, how many grams of barite did the chemist start with?
possiable answers
0
8
15
71
Answer:
The answer is 71
What is chemist?
A chemist is a person who specializes in the science of chemistry, which is the study of matter and its properties, structure, composition, behavior, and the changes it undergoes. Chemists are trained in the scientific discipline of chemistry and use their knowledge to study and manipulate matter. This can include anything from the analysis of materials for their chemical makeup, to the development of new products and processes. Chemists can work in a variety of fields, including pharmaceuticals, materials science, biochemistry, research and development, and more. They must be well-versed in the principles and theories of chemistry, as well as in the practical aspects of their work. Through their work, chemists contribute to the advancement and application of science.
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Answer: the answer is 15
Step-by-step explanation:
Number of nickels in $4.20
Answer:4
Step-by-step explanation:
Please help meee !!!!???
Answer: 19 feet
Step-by-step explanation:
The area, 266, divided by the width, 14, equals to 19 feet.
The original selling price was $171.59. The sale proteas $148.37. What is the first step in finding the percent markdown? Find the percent markdown
The original price is $171.59 and the price during sales is $148.37 then the percent markdown will be 13.53%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Original selling price = $171.59
Price during sales = $148.37
Then, the percentage markdown will be,
% markdown = (171.59 - 148.37)/171.59 × 100
= 23.22/171.59 × 100
% markdown = 13.53%
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Angie is determining the volume of a box in the shape of a rectangular prism. She finds the length is 2cm more than the width and 3 cm less than the depth. Which equation can Angie use to get the volume of the box, in cubic centimeters?
A. V = w(w+2)(w+3)
B. V = w(w+2)(w+5)
C. V = w(w-2)(w-3)
D. V = (w+2)(w+5)
The volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.
What is a rectangular Prism ?
A polyhedron with two congruent and parallel bases is known as a rectangular prism. It's also known as a cuboid.
A rectangular prism has six faces, each of which is in the shape of a rectangle and has twelve edges. It's called a prism because of its cross-section along its length.
It is given that length of the rectangular prism has length of 2 cm more than the width and 3 cm less than the depth
Let the depth be x cm
and width be y cm
Then the length will be y+2 cm and x-3 cm
y+2 = x- 3
x = y+5
A rectangular prism is a cuboid with six faces
Volume of a rectangular prism can be written as
length * width * depth
= (y+2) *x*y
= (y+2)* (y+5)*y
= (y²+2y)(y+5)
= y³ +5y²+2y²+10y
= y³ +7y² +10y cm³
Therefore the volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.
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Given the function f(x)=7(3-x)+5 what is the answer
The answer of the function f(x)=7(3-x)+5 is -7x + 26.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
Given the function;
f(x)=7(3-x)+5
To simplify the function:
First, solve parenthesis,
f(x)=21 - 7x +5
Taking, constant with constant term,
f(x) = -7x + 26
Therefore, the answer is -7x + 26.
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(Find LCM of) :
ax² - (a² + ab)x+ a²b,
bx² - (b² + bc)x+ b²c and
cx² - (c² + ac)x + c²a
Answer:
Here is answer
Step-by-step explanation:
To find the least common multiple (LCM) of three polynomials, we need to find the smallest polynomial that is divisible by all three of them.
Let's start by factoring each of the given polynomials:
ax² - (a² + ab)x+ a²b = a(x - b)x
bx² - (b² + bc)x+ b²c = b(x - c)x
cx² - (c² + ac)x + c²a = c(x - a)x
The LCM of these three polynomials is the smallest polynomial that is divisible by all three of them. In this case, the smallest such polynomial is (x - a)(x - b)(x - c)x. This is because it is divisible by each of the given polynomials and no smaller polynomial is divisible by all three of them.
Therefore, the LCM of the given polynomials is (x - a)(x - b)(x - c)x.
Evaluate. Remember Order of
Operations! (PEMDAS)
8 x 3²- (14+ 6) = [?]
Answer:
52
Step-by-step explanation:
Order of Operations says to do Parenthesis first, then exponents.
8 x 3²- (14+ 6)
= 8 x 3²- (20)
= 8 × 9 - 20
Then multiply before subtracting in this question.
= 72 - 20
= 52
what is the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order?
The final answer is that the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order is 1.54.
This is calculated by probability of independent events.
We know that any die can get any of the six sides and all the throws are independent, so their intersection is given by the product.
So, P(A and B occurring together )= P(A)P(B) if A and B are independent.
And the probability of the throws i.e. the no. of ways every throw gets a unique number is (6/6) x (5/6) x (4/6) x (3/6) x (2/6) x (1/6)
This is because, being the probability of independent events , they are multiplied.
so, the total probability is 6.5.4.3.2.1/6^6 = 1.54
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How would i solve for E
Answer:
5/13
Step-by-step explanation:
[tex]CE=\sqrt{10^2 + 24^2}=26 \\ \\ \cos E=\frac{10}{26}=\frac{5}{13}[/tex]
