A. Write each of the following decimals using digits.
21. Twenty-six hundredths
22. Nine tenths
23. Thirty hundredths
\(pls \: answer \: \)
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The scale factor of the dilation transformation of the pre-image triangle ΔDEF to the image ΔD'E'F', with the origin as the center of dilation is 3.

A dilation transformation is one in which the lengths of the sides of the pre-image are scaled up by a common factor to get the lengths of the sides of the image.

The coordinates of the vertices of the triangle ΔDEF are;

D(1, 5), E(1, 2), F(3, 2)

The length of the sides of triangle ΔDEF, making use of the difference between the non equal coordinate points, are;

DE = 5 - 2 = 3

EF = 3 - 1 = 2

The length of the side DF can be found using the formula for the distance between two points on the coordinate plane (a form of the Pythagorean Theorem), which is presented as follows;

DF = √((3 - 1)² + (2 - 5)²) = √(2² + (-3)²) = √(13)

The coordinates of the vertices of triangle ΔD'E'F' are; D'(3, 15), E'(3, 6), F'(9, 6)

Therefore; D'E' = 15 - 6 = 9

E'F' = 9 - 3 = 6

D'F' = √((9 - 3)² + (6 - 15)²) = √(6² + (-9)²) = √(9 × 13) = 3·√(13)

The scale factor, s.f. = The ratio of the corresponding sides of the triangles which is found as follows;

D'E'/DE = 9/3 = 3

E'F'/EF = 6/2 = 3

D'F'/DF = 3·√(13)/√(13) = 3

s.f. = D'E'/DE = E'F'/EF = D'F'/DF = 3

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The average credit card debt for a public school teacher is μ = 14,975 pesos and the standard deviation is σ = 5,650 pesos.

Find the probability that the teacher owes at least 6,740 pesos.

Let X be the random variable representing the credit card debt that a public school teacher has.

Then, X ~ N(14975, 5650) which means that X is normally distributed with a mean 14,975 and a  standard deviation of  5650.

Find the probability that the teacher owes at least 6,740 pesos.

This can be represented as P(X ≥ 6740).

Use the z-score formula which is given by z = (X - μ) / σ,

where X is the credit card debt, μ is the mean, σ is the standard deviation and z is the z-score corresponding to X.

So, substituting the given values,

z = (6740 - 14975) / 5650= -0.8912 (approx)

Using the z-table, the probability corresponding to this z-score is P(Z ≤ -0.8912) = 0.1866 (approx).

Therefore,P(X ≥ 6740) = 1 - P(X < 6740)= 1 - P(Z ≤ -0.8912) = 1 - 0.1866= 0.8134 (approx).

Hence, the probability that the teacher owes at least 6,740 pesos is approximately 0.8134.

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the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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Answer:

C(t) = 25+34.37t

Step-by-step explanation:

It is given that,

The monthly fee to be a member is $25 and the total cost of membership, including the joining fee, would be $300 for 8 months.

We need to write an equation for C in terms of t representing the total cost of the gym membership over t months.

At t=0, Jonathan pays $25 as joining fee.

Equation will be :

C(t) = Co+kt

Initially, Co = 25

C(t) = 25

At t = 8,

C(8) = 25 + k(8) = 300

8k = 275

k = 34.37

⇒ C(t) = 25+34.37t

Hence, this is the required equation.

The probability that all 5 customers order pepperoni pizza is 0.2457 and the probability that at least 1 customer doesn't order pepperoni pizza is 0.7543.

We can calculate the probability that all 5 customers order pepperoni pizza by multiplying the probability that each individual customer orders pepperoni pizza.

The probability of each customer ordering pepperoni pizza is 72%. Therefore, the probability that all 5 customers order pepperoni pizza is (0.72)^5 = 0.2457.

We can calculate the probability that at least 1 customer doesn't order pepperoni pizza by subtracting the probability that all 5 customers order a pepperoni pizza from 1.

Hence, The probability that at least 1 customer doesn't order pepperoni pizza is 1 - 0.2457 = 0.7543.

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Answer:

F. 625

Step-by-step explanation:

625 times 2

= 1256

round it to

= 1250

Hope this Helps

Have a nice day

Answer:

m = 3/4

Step-by-step explanation:

Start in (- 2,1) up three and four to the right. Positive slope. (Going uphill positive +, and downhill is negative - )

Answer:

0.333333...

Step-by-step explanation:

2/6 = 1/3 = 0.33333...

You can divide on paper or on a calculator 2÷6 or 1÷3 to find this. If you are allowed to use a calculator and your calculator has F>D and D>F buttons they are for converting decimals and fractions back and forth. On paper, you are doing like a long division calculation. Put 2 inside the little dividing frame and put 6 on the outside. Or 1 inside and 3 outside. See image.

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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Answer:

z=13/2

Step-by-step explanation:

Answer:

z = 6.5

Step-by-step explanation:

3z + 2 = z + 15

      -2        -2

      3z = z + 13

       -z   -z

      2z = 13

           2

         z = 6.5

Answer:

To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height, then you can easily find all four sides (two sides are each equal to the height and the other two sides are equal to the width). Multiply both the height and width by two and add the results.

Answer:

The area is 18.83 meters². The perimeter is 17.76 meters.

Step-by-step explanation:

To find the area you need to multiply the width and the length. So you need to use the equation \(5.38*3.5\). That equals 18.83. That is the area.

To find the perimeter you need to add \(5.38+5.38+3.5+3.5\). You need to use this equation because there are 4 sides; 2 lengths and 2 widths. This adds up to 17.76

Answer:

I think that the common factor in the given algebraic is a-b

Answer:

90 degrees.

Step-by-step explanation:

They right ray point is on the 90 degree number and left ray is on zero so we find the difference.

90-0=90

so it measures 90 degrees.

Answer:

<ba=180 <bc=90

Step-by-step explanation:

Answer:

The number is:

-8

Step-by-step explanation:

2(a/2 + 6 ) = 4

2*a/2 + 2*6 = 4

2a/2 + 12 = 4

a + 12 = 4

a = 4-12

a = -8

Check:

2(-8/2 + 6) = 4

2(-4+6) = 4

2*2 = 4

Answer:

The two planes have traveled the same distance.

Step-by-step explanation:

Given that:

Velocity of first plane traveling north = 100 km/h

Time taken by the plane = 2.5 hours

Velocity of second plane traveling north = 62.5 km/h

Time taken by the plane = 4 hours

To find:

Which plane traveled longer distance?

Solution:

First of all, let us have a look at the formula for finding the distance using velocity and time.

Formula is:

\(Distance = Velocity \times Time\)

Distance traveled by first plane:

\(Distance_1 = 100\times 2.5\\\Rightarrow Distance_1 = 250 \ km\)

Distance traveled by second plane:

\(Distance_2 = 62.5\times 4\\\Rightarrow Distance_2 = 250 \ km\)

Here, we can clearly see that:

\(Distance _1 = Distance _2\)

Therefore, the two planes have traveled the same distance.

With 95% confidence the population mean μ is between 48.02 and 51.98. To construct confidence interval for the population mean, we need sample mean ,sample standard deviation, sample size additionally.

Assuming we have this information, we can use the following formula to calculate the confidence interval:

Confidence interval = sample mean +/- (t-critical * (sample standard deviation / square root of sample size))

where t-critical is the value from the t-distribution with n-1 degrees of freedom that corresponds to the level of significance (alpha) and sample size (n).

For example, if we have a sample size of 100, a sample mean of 50, a sample standard deviation of 10, and a level of significance of 0.05 (two-tailed test), the t-critical value for a 95% confidence interval would be 1.984.

Plugging these values into the formula, we get:

Confidence interval = 50 +/- (1.984 * (10 / √(100))) = (48.02, 51.98)

Interpreting the confidence interval, we can say with 95% confidence that the population mean m is between 48.02 and 51.98. This means that if we were to repeat the sampling process many times and calculate the confidence interval for each sample, we would expect 95% of these intervals to contain the true population mean.

In addition to providing a range of plausible values for the population mean, the confidence interval also provides information about the precision of the estimate. The wider the confidence interval, the less precise the estimate is likely to be. The narrower the confidence interval, the more precise the estimate is likely to be.

The width of the confidence interval depends on the sample size, sample standard deviation, and level of significance. A larger sample size, a smaller sample standard deviation, or a higher level of significance will all result in a narrower confidence interval.

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Complete question is:

Filling cola bottles Refer to Exercise 80 . Construct and interpret a 95% confidence interval for the population mean μ. What additional information does the confidence interval provide?

Answer: 50 km

Step-by-step explanation: So the map has a scale of 1 cm: 20 km. Next, you look at how far they are apart and see if the scale and the distance on the map are the same measurement. In this case, they are both centimeters so they stay the same. Then, all you do is multiple the real size, 20 km, by  

2.5 /1 . Then, 20 x 2.5=50. So the answer is 50 km

Answer:

huh? no they cant both be 30 at the same time is cindy is 2 years older than marie....

Step-by-step explanation:

Answer:

In this question the value of x is given 29 so put it in the equation to get answer

\(h(x) = {x}^{2} + 4\)

put the value of x = 29 in the above equation

\(h(x) = {29}^{2} + 4\)

so after solving this equation we get our answer

\(h(x)= 841 + 4\)

\(h(x) = 845\)

Hope it helps u mate

if u like leave a thank

Answer:

the variable x=12.5

Step-by-step explanation:

so first you will insert 29 to the equation

29= x2+4

now you subtract 4 from 29

29-4= 25

since you are multiplying you have to do the opposite operation which would be division so now divide 25 by 2

25/2

now insert your answer

h(12.5)=(12.5)2+4

h would be considered 2.32

Answer:

y = - 2x + 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute (4, 5) into the partial equation

5 = - 8 + c ⇒ c = 5 + 8 = 13

y = - 2x + 13 ← equation of line

Answer:

Step-by-step explanation:

slope=-2

now using slope intercet formof equation of straight line,we get

y=mx+b

or, y=-2x + b

y + 2x =b

2x + y=b ......................   eq(i)

since the line passes through the point (4,5) it satisfies the equation (i)

y=5 and x=4 so,

equation is 2x +y =b

2*4 + 5=b

8+5=b

13=b

substituting the value of b in eq(i)

2x + y=b

2x + y=13

2x + y-13=0  is the required equation of the line.

Answer:

angle

Step-by-step explanation:

An angle consists of two rays joined together.  The rays are joined at the vertex.

Answer:

angle

Step-by-step explanation:

An angle consists of two different rays with a common endpoint.

Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.

The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:

6x+12x=180

18x=180

x=10°

Therefore, 6x= 6*10=60° and 12x=12*10=120°.

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The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

Answer:

25\(z^{4}\) + 30z³ + 29z² + 12z + 4

Step-by-step explanation:

(5z² + 3z + 2)²

= (5z² + 3z + 2)(5z² + 3z + 2)

Each term in the second factor is multiplied by each term in the first factor, that is

5z²(5z² + 3z + 2) + 3z(5z² + 3z + 2) + 2(5z² + 3z + 2) ← distribute parenthesis

= 25\(z^{4}\) + 15z³ + 10z² + 15z³ + 9z² + 6z + 10z² + 6z + 4 ← collect like terms

= 25\(z^{4}\) + 30z³ + 29z² + 12z + 4

The intersection A13−13∩{0∗1∗} is not equal to {0n1n∣n≥0}.

The claim that A13−13∩{0∗1∗}={0n1n∣n≥0} is not correct.

To see why, let us consider a counterexample. Take the string w = "0000#1000". The middle third of w is "0#1", so the string obtained by removing the middle third is "000011000". This string is not in {0n1n∣n≥0}, as there are more 0s than 1s. However, "000011000" is in A13−13, as it can be written as "0000#1000" with the middle third removed.

Therefore, the intersection A13−13∩{0∗1∗} is not equal to {0n1n∣n≥0}.

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Answer:

on which days did it rain less then one-fifth of an inch

Step-by-step explanation:

Answer:

There are 90 African animals in the zoo.

Step-by-step explanation:

172/2=86

86+4=90

Answer:

\(\huge\boxed{\text{0.17 hours}}\)

Step-by-step explanation:

We can create two ratios to find how long you can use a bike for one dollar.

Let's set up a ratio in the form \(\frac{cost}{hours}\)

We know it costs $23 to ride for 4 hours, so we can make the fraction \(\frac{23}{4}\).

We also know that for $1, we'll have some unknown time for the bike. We can represent this as \(\frac{1}{x}\).

Since the constant of proportionality has to be the same, we can set these two ratios equal to each other.

\(\frac{23}{4}=\frac{1}{x}\)

We can now solve for x by cross multiplying.

\(1 \cdot 4 = 4\\\\4 \div 32 \approx 0.17\)

So $1 will get you around 0.17 hours of bike time.

Hope this helped!

Answer:

0.17

Step-by-step explanation:

We can create two ratios to find how long you can use a bike for one dollar.

Let's set up a ratio in the form

We know it costs $23 to ride for 4 hours, so we can make the fraction .

We also know that for $1, we'll have some unknown time for the bike. We can represent this as .

Since the constant of proportionality has to be the same, we can set these two ratios equal to each other.

We can now solve for x by cross multiplying.

So $1 will get you around 0.17 hours of bike time.

have a blessed day