Which is the scale factor of the dilation?

Answer:

The pints of each of the two existing types of drinks are 22 and 88 respectively.

Step-by-step explanation:

We are given that the Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice.

Let the first type of fruit drink pints in the mixture be 'x' and the second type of fruit drink pints in the mixture be 'y'.

So, according to the question;

                                   x + y = 110

                                   x = 110 - y  ---------------- [equation 1]

                             \(0.70x+0.95y=0.90\times 110\)

                              \(70x+95y=9900\)

                              \(70(110-y)+95y=9900\)

                              \(7700-70y+95y=9900\)

                              \(25y=9900-7700\)

                                \(y=\frac{2200}{25}\)

                                y = 88

Now, putting the value of y in equation 1 we get;

                               x = 110 - y

                               x = 110 - 88 = 22

Hence, the pints of each of the two existing types of drinks are 22 and 88 respectively.

Step-by-step explanation:

the area of a triangle is baseline×height/2

in case of such a right-angled triangle we can use the sides that enclose the 90 degree angle as baseline and height.

so,

B = 8×6/2 = 8×3 = 24 yd²

the height h is 8 yd (as the picture clearly shows).

the perimeter of the base is the sum of all three sides

P = 8 + 6 + 10 = 24 yd

\(8^{3} \cdot 8^{-7} =8^{-4}=\boxed{\frac{1}{8^4}}\)

Answer: x=-16

Step-by-step explanation:

g^-1 is the inverse of the g(x) graph meaning that the x and g(x) values of the g(x) graph switch places. So in the table when  x=-2 g(x)=-16

Answer:

0

Step-by-step explanation:

2(n - 1) + 4n = 2 ( 3n - 1 )

2n - 2 + 4n = 6n - 2

6n - 2 = 6n - 2

6n - 6n = -2 + 2

0 = 0

A connected graph can be disconnected by removing vertices if and only if it is not a complete graph.

A connected graph is one where there exists a path between any pair of vertices. Removing any vertex from a complete graph will result in a disconnected graph since there will be at least one pair of vertices that are no longer connected. Therefore, a complete graph cannot be disconnected by removing vertices.

On the other hand, if a graph is not a complete graph, it means that there exist at least two vertices that are not connected by an edge. By removing these vertices, we effectively disconnect the graph since there is no longer a path between them.

Thus, it is possible to remove vertices to disconnect a graph that is not a complete graph.

A complete graph cannot be disconnected by removing vertices, while a non-complete graph can be disconnected by removing appropriate vertices.

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Answer:

20

Step-by-step explanation:

By HL and CPCTC, GF = FI, so GI = 2FI = 2(10) = 20.

The actual weight is 0.0042 pounds lighter than the labeled weight.

The actual weight of the chocolates is 0.3798 pounds, while the label on the bag states it should weigh 0.384 pounds. To determine how much lighter the actual weight is, we can calculate the difference between the two weights.

Subtracting the actual weight from the labeled weight, we get:

0.384 pounds - 0.3798 pounds = 0.0042 pounds.

Therefore, the actual weight is 0.0042 pounds lighter than the labeled weight.

It's important to note that this difference may seem small, but it can be significant depending on the context. Accuracy in labeling is crucial for various reasons, such as complying with regulations, providing precise information to consumers, and ensuring fair trade practices. Even minor discrepancies can impact trust and customer satisfaction.

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The value of the integral ∫√x/(x - 4) dx from 9 to 16 is 3.022

From the question, we have the following parameters that can be used in our computation:

∫√x/(x - 4) dx from 9 to 16

The above expression can be integrated using integration by parts method

When integrated, we have

∫√x/(x - 4) dx = 2(√x - ln(√x + 2) + ln(|√x - 2|))

Recall that the x values are from 9 to 16

This means that

∫√x/(x - 4) dx = 2(√16 - ln(√16 + 2) + ln(|√16 - 2|)) - 2(√9 - ln(√9 + 2) + ln(|√9 - 2|))

So, we have

∫√x/(x - 4) dx = 2(4 - ln(4 + 2) + ln(|4 - 2|)) - 2(3 - ln(3 + 2) + ln(|3 - 2|))

Solving further, we get

∫√x/(x - 4) dx = 2(4 - ln(6) + ln(2)) - 2(3 - ln(5) + ln(1))

Evaluate

∫√x/(x - 4) dx = 3.022

Hence, the value of the integral is 3.022

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Answer:

it might be 2,-2

Step-by-step explanation:

Answer:

11700 m²

Step-by-step explanation:

Split the shape in two. One rectangle 150x30 and one triangle 180x80.

Find the areas of both and add them:

A = bh + 1/2bh

A = 150(30) + 1/2(180)(80)

A = 4500 + 7200

A = 11700

Answer:

31.41592...

Step-by-step explanation:

If the radius of the circle is 10 inches, the circle's circumference is 31.4 because you calculate circumference as follows:

x = r * pi (3.1415926535)

Step-by-step explanation:

To find the percentage increase, we use the following formula:

percentage increase = (new value - old value) / old value * 100%

In this case, the old value is 25 and the new value is 86. So, we can plug these values into the formula:

percentage increase = (86 - 25) / 25 * 100% = 244%

Therefore, the percentage increase from 25 to 86 is approximately 244%.

Answer:

244% increase

Step-by-step explanation:

Answer:

c. y + 3 = (1/2)(x - 1)

Step-by-step explanation:

Answer:

A. \(y + 1 = (-\frac{1}{2})(x + 3)\)

Step-by-step explanation:

I used a graphing calculator. I prefer Desmos, but you can use whatever you like. I recommend Desmos or GeoGebra.

Answer:

No, 8+10=18 but, 14+10=24 which means x=14

Step-by-step explanation:

Based on the information given, the correct options will be:

a.) Mary would use the sample standard deviation to calculate a t-statistic.

c.) The value for the degrees of freedom for Mary's sample population is six.

One-sample t-test simply means a statistical hypothesis test that's used for the determination of whether an unknown population mean will be different from the specific value.

In this case, the value of the degree of freedom for the sample will be:

= (n - 1) = 7 - 1 = 6.

Also, it should be noted that Mary would use the sample standard deviation to calculate a t-statistic.

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The probability of failure on trial 9 is 0.74.

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The probability of failure on a trial is equal to 1 - the probability of success on that trial. Therefore, the probability of failure on trial 9 is 1 - 0.26 = 0.74.

Hence, the probability of failure on trial 9 is 0.74.

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Answer:

Formula:  V = 1/3πr^2h

Height: 6cm

Step-by-step explanation:

step one:

given information

volume =32π cm^#

radius=4cm

step two:

The formula is

V = 1/3πr^2h

substituting we have

32π =1/3π*4^2*h

32π=16πh/3

π cancels out

step three:

cross multiply we have

32*3=16h

divide both sides by 16 we have

96/16=h

h=6cm

Answer:

A) 7

Step-by-step explanation:

25% = 0.25

28 x 0.25 = 7

Step-by-step explanation:

q=r+rst

Rewrite the equation as 

r+rst=q

Subtract r from both sides of the equation.

r st=q−r

Divide each term by rt

(r st )/rt=(q/rt)−(r/rt)

Cancel the common factor.

(

s=(q/rt)−1/t

Answer:

Step-by-step explanation:

$18 spent on parking. 100-18=82

$42.50 on admission 80- 42.50= 39.5

20 percent of 100 is 20 so 39.5-20=19.5

12.75 so 19.4-12.75=6.65

1.75x=6.65

x=3.8 so basically henry played 3 games

Answer:

1. I would think it would be a appropriate to use a normal model to figure this out because sometimes when you are using stuff online you can get the same number like 20 times in a row, whereas, if you use a real dice, you most likely won't roll the same number 20 times.

2. { sorry two doesn't make sense }

Answer:    A

Step-by-step explanation:

8,4 cause they in there intersect there

Answer:

320 pounds sterling

Step-by-step explanation:

All you have to do is $380.80 divided by $1.19 which is equal to one pound sterling. Hope this helps!

Answer:

Multiply the radius by 2

Step-by-step explanation:

The diameter of a circle is 2times the radius of the circle. Do you know the radius? If so multiply that number by 2 and get the answer

Answer:

The given shape is Trapezium

Area of Trapezium= 1/2h(L1+L2)

=1/2×7×(11+3

=1/2×7×14

=49

Your answer is 49

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

The probability that at least one of your lights is​ defective is .

The probability of precisely x successes on n repeated trials is known as a binomial probability, and X can only have two possible outcomes.

\(P(X=x)=^nC_rp^x(1-p)^{n-r}\)

Where \(^nC_r\) is the number of different combinations of x objects from a set of n elements and p is the probability.

Now, here 6% lights did not work, so

p=6/100=0.06

n=5

Now, finding the probability that at least one of your lights is​ defective. Either one bulb is defective or no one is defective.

\(P(X=0)+P(x\geq 1)=1\\P(x\geq 1)=1-P(X=0)\)

Now, finding probability of no defective,

\(P(X=0)=^5C_00.06^0(1-0.06)^{5}\\=0.7339\\P(X\geq 1)=1-0.7339\\=0.2661\)

Now, finding the percentage probability,

\(0.2661\times100=26.61\)%

Therefore, the probability that at least one of your lights is​ defective is 26.61%.

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The given question is incomplete here is the complete question:

You purchased a​ five-pack of new light bulbs that were recalled because 6​% of the lights did not work. What is the probability that at least one of your lights is​ defective?.

The area of the enlarged rectangle is 588 square units.

The original rectangle has a length of 8 units and a width of 6 units.

To find the area of the enlarged rectangle, we need to multiply the length and width of the original rectangle by the scale factor of 3.5.

Enlarging the length: 8 * 3.5 = 28 units.

Enlarging the width: 6 * 3.5 = 21 units.

The enlarged rectangle has a length of 28 units and a width of 21 units.

To find the area, we multiply the length and width of the enlarged rectangle: 28 * 21 = 588 square units.

Therefore, the area of the enlarged rectangle is 588 square units.

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