DIVIDING INTEGERS. Sarah and Anna both ran five laps of a race. When Anna finished, Sarah was 15 meters behind Anna suppose Sarah fell behind the same number of meters during each lap write an integer that describes how far is Sarah fell behind each lap

The lines or segments which are secant to a circle are:  

AK, TW, RN & UN

A line that crosses a circle at two different locations is referred to as a "secant of a circle" in geometry. The Latin verb "secare," which meaning "to cut," is where the English term "secant" originates.

More technically, a secant of a circle is a line that crosses it twice, whereas a tangent of a circle is a line that crosses it only once. A circle's diameter is a chord that runs through its center, whereas a chord of a circle is a line segment connecting two locations on the circle.

Given that,

Two circle which contains various tangents, normal & secants

As we know from the definition of secant it intersect the circle at two points,

Line segments AK, TW, RN & UN are intersecting the circle at two points,

so all this segments are secant of the circle.

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Answer: Since Connor gets 69% of the money, Maria gets the remaining 31%:

100% - 69% = 31%

Let's first find out how much money Maria makes:

Maria's share = 31% of $595.54

Maria's share = 0.31 x $595.54

Maria's share = $184.61

Now, to find out how much Connor makes, we can subtract Maria's share from the total:

Connor's share = Total - Maria's share

Connor's share = $595.54 - $184.61

Connor's share = $410.93

Therefore, Connor makes about $410.93 (rounded to the nearest dollar).

Step-by-step explanation:

Answer:

14.4

Step-by-step explanation:

=24 * 60/100
=14.4

Answer:

14.4

Step-by-step explanation:

[tex]\frac{24}{10} = 10[/tex]% of 24

6[tex]\frac{24}{10} = 60[/tex]% of 24

Answer:

[tex]416 \;in^2[/tex]

Step-by-step explanation:

The surface area of the rectangular prism

[tex]S = 2(lw + lh + wh)[/tex]

where

l = length = 12 in

w = width = 10 in

h = height = 4 in

Therefore

[tex]S = 2(12\cdot 10 \;+ \; 12\cdot 4 \;+\;10 \cdot 4)\\\\= 2(120 + 48 + 40)\\\\= 2 (208)\\\\= 416 \: in^2[/tex]

Answer:

55

Step-by-step explanation:

The ? angle is 55 degrees since every triangle's angles add up to 180 degrees. We have 2 angles, one with 70 and another with 55, so we add them to get 125. Then we subtract 125 from the total angle of a triangle, 180-125, to get 55.

the answer is 55

they have the same degrees hope this helps

Answer:

x = 13

Step-by-step explanation:

Let's simplify and solve for x:

4(x+56.5) = 30x - 112

First, we distribute the 4:

4x + 4(56.5) = 30x - 112

Simplifying the expression:

4x + 226 = 30x - 112

Now we move all the x terms to one side and all the constants to the other:

226 + 112 = 30x - 4x

338 = 26x

Finally, we solve for x by dividing both sides by 26:

x = 13

Therefore, the solution to the equation 4(x+56.5)=30x-112 is x = 13.

Answer:

x=9.94

Step-by-step explanation:

4x + 226 = 30x - 112
226+112 = 34x
338 = 34x
338/34=x
9.94=x

Answer:

circumference  = 8 inches

Step-by-step explanation:

75% = 75/100 = 3/4

Let C be the circumference

3/4 C = 6

Multiply both sides by 4/3

C =

Of the first 100 vehicles, there are nine convertible green cars.

The sequence of green cars:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99

The sequence of convertible cars:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100.

Convertible and Green cars (in the very first 100 cars):

12, 24, 36, 48, 60, 72, 84, and 96.

Thus, of the first 100 vehicles of auto assembly line, there are nine convertible green cars.

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The complete question is-

On an automobile assembly line, every third car is green. Every fourth car is a convertible. How many cars out of the first 100 will be green convertibles?

Hence, a 93% confidence range for the actual proportional difference between the two populations equation (represented by the two samples) is between -0.086 and 0.142.

A mathematical equation connects two statements with the equals sign (=), which stands for equivalence. The equivalence of two mathematical propositions is established by a mathematical assertion that is utilized in algebraic equations. For instance, the equal sign separates the numbers 3x + 5 and 14 in equation 3x + 5 = 14. Use a mathematical formula to understand the relationship between the two sentences written on opposite sides of a letter. Usually, the program's particular logo matches it. A good example is 2x - 4 = 2.

For the initial example:

Sample proportion: 0.649 (p1 = 24/37)

Standard deviation SE1 is equal to

[tex]\sqrt{(p^1*(1-p^1))} /n1=\sqrt{(0.649*(1-0.649))/37)0.087}[/tex]

Regarding the second example:

P2 = 54/87 0.621 is the sample proportion.

The standard deviation SE2 is equal to

[tex]\sqrt{(p^2*(1-p^2))} /n2=\sqrt{(0.621*(1-0.621))/87)0.72}[/tex]

The crucial value for a 93% confidence interval has to be calculated next. We may use the conventional normal distribution and large sample size to obtain the z-value that represents the center 93% of the distribution:

[tex]1.812z=invNorm(\frac{1+0.93}{2} )[/tex]

We can finally determine the confidence interval:

CI is equal to (p1-p2) z*sqrt(SE12 + SE22)

CI is calculated as (0.649 - 0.621) 1.812*sqrt(0.0872 + 0.0722)

CI = 0.028 ± 0.114

CI = (−0.086, 0.142)

The real proportional difference between the two populations (represented by the two samples) thus lies between -0.086 and 0.142, with a 93% confidence interval.

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Answer:

Below

Step-by-step explanation:

1  8/10  = 18/10

18 / 10   pound  *  $ 4.10 / pound  =  (18 * 4.1) / 10 =  73.8 /10 = $ 7.38

( see how the unit 'pound' cancels out and you are left with  $  ???)

The equation of the line crossing (3, 1 / 2)(5, 5) is y = 9 / 4 x  - 25 / 4.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Hence, let's find the equation of the line crossing (3, 1 / 2)(5, 5).

m = 5 - 1 / 2 / 5 - 3

m = 9 / 2 × 1 / 2

m = 9  / 4

Hence, let's find the y-intercept using (5, 5)

y = 9 / 4 x + b

5 = 9 / 4(5) + b

5 - 45 / 4 = b

b =  20 - 45/ 4

b = - 25 / 4

Therefore, the equation of the line is y = 9 / 4 x  - 25 / 4.

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The equations that have the same value of x as the given equation are:

18x - 9 = 72

3(6x - 3) = 72

x = 4.5

The correct options are the third, fourth, and fifth options

From the question, we are to determine the equations that have the same value of x as the given equation

To solve the given equation, we can begin by simplifying it:

3/5 (30 x - 15) = 72

Multiplying both sides by 5/3, we get:

30 x - 15 = 120

Adding 15 to both sides, we get:

30 x = 135

Dividing both sides by 30, we get:

x = 4.5

Now, to check which equations have the same value of x as the above result, we can substitute x = 4.5 in each option and see which ones result in a true statement.

Substituting x = 4.5, we get:

18(4.5) - 15 = 72

81 - 15 = 72

This is not a true statement, so this option is not correct.

Substituting x = 4.5, we get:

50(4.5) - 25 = 72

225 - 25 = 72

This is not a true statement, so this option is not correct.

Substituting x = 4.5, we get:

18(4.5) - 9 = 72

81 - 9 = 72

This is a true statement, so this option is correct.

Substituting x = 4.5, we get:

3(6(4.5) - 3) = 72

3(24) = 72

This is a true statement, so this option is correct.

4.5 = 4.5

This is a true statement, so this option is correct.

Hence, the equations are:

18x - 9 = 72

3(6x - 3) = 72

x = 4.5

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The table that shows a proportional relationship is Table A.

A proportional relationship is a type of relationship between two variables in which the ratio of their values remains constant. In other words, as one variable increases or decreases, the other variable also increases or decreases in proportion to it.

In table A, we see that :

= 150 / 3

= 50

= 200 / 4

= 50

= 250 / 5

= 50

Every single value of y, gives the same value of x so this means that the table shows a proportional relationship.

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The coordinates of the points on the number line are given as follows:

Point C is exactly halfway between 0 and 1, hence it's coordinate is given as follows:

C = 0.5.

C is also the third dot between 0 and 0.5, hence the amount represented by each space is given as follows:

0.5/3 = 1/6.

Point B is one space to the left of 0, hence it's coordinate is given as follows:

B = -1/6.

Point A is three spaces to the left of point B, hence it's coordinate is given as follows:

A = -1/6 - 3 x 1/6 = -4/6 = -2/3.

Point D is two spaces to the right of 1, hence:

D = 1 + 2x 1/6 = 1 + 1/3 = 4/3.

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The correct answer is (C) OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.

What is line?

A one-dimensional geometric figure that consists of infinitely many points arranged in a straight path or direction.

In this case, we are reflecting across the line y = -2, which is two units below the x-axis. Therefore, the y-coordinate of each point in the preimage will be changed by 2 units after reflection.

The coordinates of L are (-1, -6), and after reflecting across y = -2, the y-coordinate will become

-6 + 2 = -4

Therefore, the image of L, L', will have coordinates (-1, -4).

Looking at the given options:

A. L'(-3, 6) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.

B. OL'(-1,6) - This point is above the reflected line y=-2, so it cannot be the reflection of L.

C. OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.

D. OL(1, 2) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.

Therefore, the correct answer is option C: L'(-1, -4).

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Answer:-(-1,026/3

Step-by-step explanation:

The number of possible outcomes is 10.

To find the number of possible outcomes find the number of outcomes when the coin is flipped and the number of outcomes when the spinner is spinning.

Multiply the number of outcomes from the coin by the number of outcomes from the spinner.  

Here we have

Enola is designing a new board game,

She flips a coin and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday    

No of possible outcomes when a coin is flipped = 2 [Head and Tail]  

No of possible outcomes when she spins a spinner = 5

[ i.e Monday, Tuesday, Wednesday, Thursday, Friday ]  

Hence, No of out comes = 2 × 5 = 10

Therefore,

The number of possible outcomes is 10.

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The farmer's market originally had 400 peaches on hand.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.

Let's use x to represent the original number of peaches the farmer's market had on hand.

We know that the farmer's market sold 35% of its produce, which means it sold 0.35x peaches. The remaining number of peaches can be calculated by subtracting the number of peaches sold from the original number of peaches:

remaining peaches = x - 0.35x

We also know that there are 260 peaches remaining, so we can set up an equation:

260 = x - 0.35x

Simplifying this equation, we can combine like terms:

260 = 0.65x

To solve for x, we need to isolate the variable by dividing both sides by 0.65:

x = 260 / 0.65

x = 400

Therefore, the farmer's market originally had 400 peaches on hand.

To explain how we used equivalent ratios, we used the fact that the farmer's market sold 35% of its produce. This can be represented as a ratio of 35/100 or 0.35. We then used this ratio to find the number of peaches sold, which is 0.35x. We also used the fact that the remaining peaches are the original peaches minus the peaches sold, or x - 0.35x. Finally, we set up an equation using the remaining peaches and solved for x to find the original number of peaches.

Hence, the farmer's market originally had 400 peaches on hand.

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The solution is, in PRYZ square, the value of m∠YKZ = 90.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

Remember that

In a Square

All sides are equal

Diagonals bisect each other perpendicularly

so

Find out KY

In the right triangle RYK

Applying the Pythagorean Theorem

RY^2=RK^2+KY^2

substitute given values

13^2=5^2+KY^2

KY^2=13^2-5^2

KY^2=144

KY=12

Find out PK

Remember that

Diagonals bisect each other perpendicularly

that means

PK=KY=12

Remember that

Diagonals bisect each other perpendicularly

so, that means

m∠YKZ = 90

Hence, The solution is, in PRYZ square, the value of m∠YKZ = 90.

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Answer:

200 x 7 = 1,400 x = 7 because there are 7 days in a week

Step-by-step explanation:

The right response is B. It is the graph of f(x) scaled down by 11 units.

For any given value of x, the output of f(x) is subtracted by 11 to get the function g(x) = f(x) - 11.

The result is the same as the input for the function f(x) = x. Thus, if we take 11 out of the result, we get:

g(x) = f(x) - 11 = x - 11

In other words, the graph of g(x) is the graph of f(x), 11 units lower.

Thus, assertion B is the correct one. It is the graph of f(x) scaled down by 11 units.

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The time at which Neo reaches the work destination is A = 8 : 15 AM

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the time at which Neo reaches the work destination be A

Now , the time at which Neo leaves home = 6 : 45 AM

And , the distance between Neo and work = 45 miles

where the speed of Neo is S = 30 miles per hour

So , the distance traveled by Neo in 1 hour = 30 miles

The distance traveled by Neo in 1.5 hours = 45 miles

Therefore , the time required by Neo to reach office is 1.5 hours

And , the time at which Neo reaches the work destination A = 6 : 45 AM + 1.5 hours

On simplifying the equation , we get

The time at which Neo reaches the work destination A = 8 : 15 AM

Hence , the equation is A = 8 : 15 AM

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Since the denominator of the expression (1 + 0.1t) cannot be zero, the domain of the model is between t = 0 and t = -10.

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

(b) We must assess the model at t = 0 in order to determine the starting number of elk in the herd:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(0))/(1 + 0.1(0))

P = 10/1

P = 10

(c) We can easily enter the relevant values of t into the model to determine the populations of elk after 25, 59, and 113 years, then round the results to the nearest integer.

When t = 25:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(25))/(1 + 0.1(25))

P ≈ 47

When t = 59:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(59))/(1 + 0.1(59))

P ≈ 189

When t = 113:

P = (10 + 3.3t)/(1 + 0.1t)

P = (10 + 3.3(113))/(1 + 0.1(113))

P ≈ 458

(d) We can use the expression's limit as t approaches infinity to determine the expected population limit:

lim P as t → ∞ = lim (10 + 3.3t)/(1 + 0.1t) as t → ∞

Using L'Hopital's rule, we can find that the limit is equal to:

lim P as t → ∞ = lim 3.3/0.1 as t → ∞

lim P as t → ∞ = 33

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11)  (A) a t-interval for a difference between means for independent samples.

12) the appropriate t-statistic is (C) 1.98.

13) option (c)

The central limit theorem is a principle in probability theory that states that the distribution of sample means will eventually approximate a normal distribution as the sample size becomes larger.

11) The type of study being conducted by Ron is a completely randomized design, where he randomly assigns the two types of golf balls (new and current) to two separate groups and then compares the mean driving distances between the two groups.

The appropriate t-interval for inference is (A) a t-interval for a difference between means for independent samples.

12) To test the hypothesis of whether there is a significant difference in mean driving distance between the new golf balls and the old golf balls, we need to calculate the appropriate t-statistic.

The formula for the t-statistic for a difference between means for independent samples is:

[tex]t = (x_1 - x_2) / [s1^2/n1 + s_2^2/n_2]^{0.5}[/tex]

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes for the two groups.

Using the given data, we have:

x1 = 203.5 yards, x2 = 197.4 yards

s1 = 5.6 yards, s2 = 10.3 yards

n1 = n2 = 30

Substituting these values into the formula, we get:

[tex]t = (203.5 - 197.4) / [(5.6)^2/30 + 10.3^2/30]^{0.5} = 1.98[/tex]

Therefore, the appropriate t-statistic is (C) 1.98.

13) The correct statement about the study being conducted by Ron is (C) The central limit theorem tells us that the sampling distribution of driving distance for each of the individual samples of balls will be approximately normal.

Hence, The answers to the question:
11)  (A) a t-interval for a difference between means for independent samples.

12) the appropriate t-statistic is (C) 1.98.

13) option (c)

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Answer: c

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

area = width x length
15 = w x w-2
15 = 5 x 3
3 is 2 less than 5, and if you multiply them together, you get the area, 15

The mass of each bun is 50g.

Two or more expressions with an Equal sign is called as Equation.

Given that the total mass of 2 loaves of bread and 5 buns is 650g.

The 2 loaves of bread weigh 400 g.

We need to find the mass of each bun.

2 loaves of bread + 5 buns = 650g

2 loaves of bread = 400g

5 buns = 650g - 400g

=250g

1 bun = 250/ 5

= 50g

The mass of each bun is 50g.

Hence, the mass of each bun is 50g.

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Complete question

The total mass of 2 loaves of bread and 5 buns is 650 g. The 2 loaves of bread weigh 400 g. What is the mass of each bun?

Answer:

Step-by-step explanation:

To use elimination method, we need to eliminate one of the variables (x or y) by adding or subtracting the two equations. To do this, the coefficients of one of the variables in the two equations should be the same or opposite.

Looking at the two equations:

Equation #1: 2x + 18y = -9

Equation #2: 4x + 18y = -27

We can see that the coefficients of y are already the same in both equations. So, we can eliminate y by subtracting Equation #1 from Equation #2.

However, to do this we need to make sure that the coefficients of x in the two equations are opposites, i.e., one is positive and one is negative.

Therefore, the first step we could take to solve this system using elimination is to multiply Equation #1 by -2 to get:

-4x - 36y = 18

Now the coefficients of x in the two equations are opposites, so we can subtract Equation #1 from Equation #2 to eliminate y and solve for x.

So, the correct answer is:

Multiply equation #1 by -2.

The algebraic expressions for the given questions are found as:

1) g/4 + 15.

2) 6 - y + 3

3) d * 8

What are algebraic expressions?

A mathematical expression made up of variables, constant algebraic numbers, and algebraic operations are known as an algebraic expression. Everything with a variable value is anything whose value changes over time. Variables in expressions are often represented by letters of the alphabet. Finding the simplified term of the given expression is the goal of simplifying the algebraic expression. We must first understand how to join like terms, factor a number, and the order of operations before we can factorise or simplify the expression. When like terms are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.

1) The quotient of g and 4 is given by g/4.

Now, this is added to 15.

So the algebraic expression is g/4 + 15.

2) The difference between y and 3 is y - 3.

Now from 6, this difference is subtracted.

So the expression becomes,

6 - (y-3) = 6 - y + 3

3) The product of two numbers is found by multiplying the numbers.

  So the expression is :

      d * 8

Therefore the algebraic expressions for the given questions are found according to the given statements.

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The proportional relationship between distance traveled and liters spent is given as follows:

y = 0.08x.

A proportional relationship is defined by a linear model with intercept of zero as follows:

y = kx.

In which k is the constant of proportionality.

Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes, hence the constant is given as follows:

k = 1/12.5

k = 0.08.

Then the equation is given as follows:

y = 0.08x.

In which:

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If the retailer pays the invoice within 20 days and takes the discount, the net amount due is $11,656.

The sale's "6/20, n/30" clause allows the retailer to choose between paying the invoice in full within 30 days or taking advantage of a 6% discount if they do it within 20 days. If the bill is paid by the 20th day, we can determine the net amount owed as follows:

Then, we multiply the invoice amount by the discount rate to determine the amount of the discount:

Discount: $744 ($12.400 x 0.06)

The amount owed if the discount is taken is then determined by deducting the discount from the invoice amount:

Discounted amount due: $12,400 - $744 = $11,656

The net amount owed is therefore $11,656 assuming the store pays the invoice within 20 days and applies the reduction.

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