Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in one yard?

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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Answer:

Explanations:

a) The scientific notation is generally expressed as;

A is any real numbers between 1 and 10

n is an integer

Given that the total surface area of North America is 9,540,000 square miles. This is expressed in scientific form as;

From the scientific notation, A = 9.54 and n = 6

b) Given the scientific notation as shown:

Writing in standard form means writing in the normal way we write numbers/decimals. Hence;

the scale factor from T to S = 1/2

Explanation:

Let the coordinate of R = (x, y)

Figure S is a scaled copy of R using a scale factor of 3:

S = 3(x, y)

S = (3x, 3y)

Figure T is a scaled copy of S using a scale factor of 2:

S = (3x, 3y)

T = 2(3x, 3y)

T = (6x, 6y)

The scale factor from T to S:

from (6x, 6y) to (3x, 3y): old to new

x axis: new/ old = 3x/6x = 1/2

y axis: new/ old = 3y/6y = 1/2

1/2(6x, 6y) will give (3x, 3y)

Therefore, the scale factor from T to S = 1/2

The length of shorter side is 2.8 inch.

We have,

A rectangular room is 28 feet by 32 feet.

The Perimeter of scale drawing of room is 12 inches.

So, the perimeter of room

= 2(l +w)

= 2(28+ 32)

= 2(60)

= 120 feet

So, the scale factor is

= 120 / 12

= 10 inches

Thus, the length of shorter side is

= 28/10

= 2.8 inch

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Answer:

0.87

Step-by-step explanation:

Given:

A composed figure of a rectangle, semicircle and another semicircle removed.

To find:

The area of the given figure.

Solution:

From the given figure it is clear that the diameter of semicircle and removed semicircle are same, i.e. 8 cm.

Since the diameter of semicircle are equal, therefore their area is also equal.

The area of the given figure is:

A = Area of the rectangle - Area of removed semi circle + Area of semicircle

A = Area of the rectangle - Area of semicircle + Area of semicircle

A = Area of the rectangle

We know that, the area of a rectangle is

\(A=length\times width\)

The length of the rectangle is 14 units and width is 8 units. So, the area of composed figure is

\(A=14\times 8\)

\(A=112\)

Therefore, the area of the combined figure is 112 sq. units.

Answer:

a) 12 ft for the length and the width

b) 7 ft as the length for each side

Step-by-step explanation:

a) Area = length x width

Since the shape is a square, that means that the length and the width have to be the same.

Because of this you have to square root 144 and you get 12 since 12x12 = 144.

b) For perimeter, this is the sum of all sides. Since a square has 4 sides and all these sides must be the same length since the shape is a square, then you have to do 28 ÷ 4 and you get 7 as your answer

Answer: 16 • (x - 2) • (x + 2) • (x - 5)

Step-by-step explanation: 1

(((2•(x-2)•(x+2))•4)•(x-5))•2

STEP

2

:

Equation at the end of step 2

((2•(x-2)•(x+2)•4)•(x-5))•2

STEP

3

:

Equation at the end of step 3

(8 • (x - 2) • (x + 2) • (x - 5)) • 2

STEP

4

:

Equation at the end of step 4

8 • (x - 2) • (x + 2) • (x - 5) • 2

STEP

5

:

Final result :

16 • (x - 2) • (x + 2) • (x - 5)

The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let Ф represent the angle Elijah makes with the ground, hence:

tanФ = 1.45/0.8

Ф = 61.11°

The angle of elevation to the building is 61.11°. Let h represent the height of the building.

tan(61.11°) = h/8.25

h = 14.95

The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.

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Answer:

Step-by-step explanation:

You take items out of a square root if you have a pair of numbers or if you know the square root.  

\(\sqrt{48b^{7} }\)=\(\sqrt{4*4*3*bbbbbbb}\)

So I know the \(\sqrt{4}\)=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3

Now for the b's for every pair there are, you can take that out.  There are 3 pairs of b's so b³ is outside and one b is left inside.

Answer:

4b³\(\sqrt{3b}\)

Answer:

3/4

Step-by-step explanation:

The 0 <= theta <= pi/2 makes it so the angle must be in the first quadrant. From there, you can use the fact that sin = opposite / hypotenuse.

Thus the opposite side length would be 5, the hypotenuse would be 5, and the adjacent side length would be 3 (by Pythagorean theorem).

Recall that cot = cotangent = 1 / tan. And recall that tan is opposite of adjacent. So tan(theta) = 4/3, and cot (theta) = 3/4.

We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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The correct measure of m<ABD = 79degrees

The measure of m<DBC  and m<ABC are 45 and 34degrees respectively.

Find the diagram to the question attached.

From the diagram, we are given the following measures;

m<DBC = 5x + 4

m<ABC = 8x - 3

m<ABD = 79degrees

From the diagram, we can see that;

m<DBC + m<CBA = m<ABD

5x + 4 + 8x - 3 = 79

13x + 1 = 79

13x = 79 - 1

13x = 78

x = 78/13

x = 6

Get the measure of m<ABC

m<ABC = 8x - 3

m<ABC = 8(6) - 3

m<ABC = 45 degrees

Get the measure of m<DBC

m<DBC = 5x + 4

m<DBC = 5(6) + 4

m<DBC = 34degrees

Hence the measure of m<DBC  and m<ABC are 45 and 34degrees respectively.

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The answer of the given question based on the scatterplot for determining  when she will reach 10,000 songs the answer is Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

Slope is  measure of  steepness or incline of  line. In geometry and mathematics, slope is defined as  ratio of the change in  y-coordinates to  change in  x-coordinates between two distinct points on  line. This is often represented by  letter "m".

To determine when Maria will reach 10,000 songs, we need to find the point on the line of best fit where the y-value is 10,000.

From the scatterplot, we can estimate that the line of best fit intersects the y-axis at approximately 2000. This means that the initial number of songs downloaded was 2000.

Next, we need to find the slope of the line of best fit. Let's choose the points (5, 6500) and (10, 9500).

The slope of the line passing through these two points is:

slope = (y2 - y1)/(x2 - x1) = (9500 - 6500)/(10 - 5) = 600 songs per month

This means that Maria is downloading 600 songs per month on average.

Finally, we can use the slope-intercept form of a line to find the x-value when the y-value is 10,000:

y = mx + b

10,000 = 600x + 2000

8000 = 600x

x = 13.33

Therefore, Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

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Answer:

y = 40, x = 9

Step-by-step explanation:

2(3y)+2(2y-20)=360

y = 40

2x=18

x = 9

0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.

Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.

Given that,

Standard deviation (σ) = 5.2 oz

mean (μ) = 10 oz

Number of students (n) = 120

As we know,

P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])

                        = P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])

                        = P (z > 1.86)

                        = 1 - P ( z < 1.86)

                        = 1 - 0.862394

                        = 0.137606

Thus, P( z > 12.7 oz.) = 0.137606

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The meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds

The functions are given as:

So, the interpretation of the function c(p(t)) is

The number of calories burned doing push-ups in t seconds

In c(p(45)), the value of t is 45

Hence, the meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds

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Answer:

$13,817.60

Step-by-step explanation:

Interest earned = $12,700 × \(\frac{8.8}{100}\) × 1

                          = $1,117.60

Total earned = $1,117.60 + $12,700

                      = $13,817.60

Answer:

23. Similar as well as congruent triangle

25. Conguent triangle

Step-by-step explanation:

Answers:

23. Not enough information

25. Congruent (by the HL theorem)

HL = hypotenuse leg

=============================================

Explanation for problem 23.

Check out figure 1 shown below.

I have marked the given diagram with light blue and light pink to show which angles are congruent.

Because lines UN and TC are parallel, we know the following alternate interior pairs are congruent.

Therefore, we can establish one link of paired congruent angles of the triangles LNU and TCH. However, we cannot determine any other angle pairings. Why not? Because we don't know if segment UL is parallel to segment TH. If they were parallel, then we could establish something like angle LUN = angle CHT as one alternate interior pairing.

But again, we don't know if UL is parallel to TH. The arrow markers aren't shown for these segments.

Therefore, we simply don't have enough information to determine if the triangles are similar or congruent.

----------------------------------------

Explanation for problem 25.

Luckily this problem will provide sufficient info to prove the triangles KSR and ISR are congruent.

We start with the given info that KR = SI due to the identical tickmarks. This represents one node in the flowchart (see figure 2).

Another node is angle RKS = angle RIS because both are right angles, aka 90 degree angles.

A third node is SR = SR because of the reflexive property.

Those three nodes then feed into the final conclusion node that triangle KSR = triangle ISR. The reasoning is "HL theorem" where HL = hypotenuse leg. This theorem works for right triangles only.

Take note how I structured the proof so that it flows from top to bottom. The three nodes side by side are related so they share the same row.

There are many other ways to make the flowchart, so don't feel obligated to use this format. Use whatever works best for you.

There is no day when the Number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2. on Day 5, Location 2 sold 850 cupcakes.

(a) To determine the number of cupcakes sold at each location on Day 5, we substitute x = 5 into the equations:

For Location 1:

y = 150x + 200

y = 150(5) + 200

y = 750 + 200

y = 950

Therefore, on Day 5, Location 1 sold 950 cupcakes.

For Location 2:

y = 150x + 100

y = 150(5) + 100

y = 750 + 100

y = 850

Therefore, on Day 5, Location 2 sold 850 cupcakes.

(b) To find the day when the number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2, we set the two equations equal to each other:

150x + 200 = 150x + 100

We can see that the variable x cancels out, which means the value of x doesn't matter in this case. The equation simplifies to:

200 = 100

However, this equation is not true. It implies that the number of cupcakes sold at Location 1 can never be equal to the number of cupcakes sold at Location 2.

Therefore, there is no day when the number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2.

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Note the full question may be :

A local bakery keeps track of the number of cupcakes sold each day at two different locations. At Location 1, the number of cupcakes sold is represented by the equation y = 150x + 200, where x represents the number of days and y represents the number of cupcakes sold. At Location 2, the number of cupcakes sold is represented by the equation y = 150x + 100.

(a) Determine the number of cupcakes sold at each location on Day 5.

(b) On which day will the number of cupcakes sold at Location 1 be equal to the number of cupcakes sold at Location 2?            

The set which could represent the range of this function is: 2) {2, -8, 42, -208,......}.

Based on the information provided, we have the following function and function rule:

Function, f(1) = 2

Function, f(n) = -5f(n - 1) + 2

When the value of n = 2, we have:

Function, f(n) = -5f(n - 1) + 2

Function, f(2) = -5f(2 - 1) + 2

Function, f(2) = -5f(1) + 2

Function, f(2) = -5(2) + 2

Function, f(2) = -10 + 2

Function, f(2) = -8

When the value of n = 3, we have:

Function, f(n) = -5f(n - 1) + 2

Function, f(2) = -5f(3 - 1) + 2

Function, f(2) = -5f(2) + 2

Function, f(2) = -5(-8) + 2

Function, f(2) = 40 + 2

Function, f(2) = 42

When the value of n = 4, we have:

Function, f(n) = -5f(n - 1) + 2

Function, f(2) = -5f(4 - 1) + 2

Function, f(2) = -5f(3) + 2

Function, f(2) = -5(42) + 2

Function, f(2) = -210 + 2

Function, f(2) = -208

Therefore, the range in interval notation is given by {2, -8, 42, -208,......}.

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Step-by-step explanation:

By Intersecting Chord Theorem,

5 * x = 10 * 4.

Hence, x = 8.

Answer:

Step-by-step explanation:

Since EF = 20 and E is at 4

F is at:

Answer:

a. Let X be the length of a wooden pole produced for electricity networks in rural areas. The probability of a pole being rejected because it is too short is 0.02, and the probability of a pole being rejected because it is too long is 0.05. The acceptable range is between 6.3 m and 7.5 m. We can find the mean and standard deviation of X as follows:

First, we need to find the z-score corresponding to the lower bound of the acceptable range:

z1 = (6.3 - μ) / σ

Similarly, we need to find the z-score corresponding to the upper bound of the acceptable range:

z2 = (7.5 - μ) / σ

Using a standard normal table, we can find the values of z1 and z2 that correspond to the probabilities of 0.02 and 0.95, respectively:

z1 = -2.05

z2 = 1.64

Solving for μ and σ, we get:

z1 = (6.3 - μ) / σ => μ = 6.3 + 2.05σ

z2 = (7.5 - μ) / σ => σ = (7.5 - 6.3) / 1.64 = 0.74

Therefore, the mean and standard deviation of X are:

μ = 6.3 + 2.05(0.74) = 7.6 m

σ = 0.74 m

b. Let Y be the number of rejected poles in a sample of 20 poles. Y follows a binomial distribution with parameters n = 20 and p = 0.02 + 0.05 = 0.07. The probability of finding 2 rejected poles in a sample of 20 poles is:

P(Y = 2) = (20 choose 2) * 0.07^2 * 0.93^18 = 0.242

The probability of finding 2 rejected poles in a sample of 20 poles is 0.242.

The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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The value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

The quadratic equation is given as:

–3 = –x^2 + 2x

Rewrite the equation as:

x^2 - 2x - 3 = 0

A quadratic equation is represented as;

ax^2 + bx + c = 0

So, we have

a = 1

b = -2

c = -3

The discriminant is

d = b^2 - 4ac

So, we have

d = (-2)^2 - 4 * 1 * -3

Evaluate

d = 16

Hence, the value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

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Answer:

16

Step-by-step explanation:

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

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p-value is a measure of the probability that an observed difference could have occurred just by random chance.