Nancy and Katie took turns driving to Digitopolis. Nancy drove 9 out of every 13 miles traveled. By the time they reached Digitopolis, Katie had driven 25 fewer miles than Nancy. How many miles did Nancy drive? I need the answer ASAP! THANK YOU! I'll give brainliest!❤️

Answer:

the answer will be

b.)

4 = -6x+3y+3x

4 = -3x+3y

3y = 3x+4

y. = x+4/3

Answer:

.........................

(a) To construct an 80% confidence interval about the population mean (μ) when the sample size (n) is 13, we can use the t-distribution since the population standard deviation is unknown.

The formula for the confidence interval is:Confidence Interval = X ± (t * (s / sqrt(n)))where X is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution corresponding to the desired confidence level.Since the sample size is small (n = 13), we will use n - 1 degrees of freedom for the t-distribution. From the t-table or a t-distribution calculator, for an 80% confidence level and 12 degrees of freedom, the critical value is approximately 1.782.Substituting the values:

Lower bound: 112 - (1.782 * (10 / sqrt(13)))

Upper bound: 112 + (1.782 * (10 / sqrt(13)))

Calculating the values, the 80% confidence interval about μ when n = 13 is approximately:Lower bound: 106.7

Upper bound: 117.3(b) To construct an 80% confidence interval about the population proportion (p) when the sample size (n) is 24, we can use the normal distribution approximation for large sample sizes. The formula for the confidence interval is:Confidence Interval = p ± (z * sqrt((p * (1 - p)) / n)From the standard normal distribution, for an 80% confidence level, the critical value is approximately 1.282.Substituting the values:

Lower bound: p - (1.282 * sqrt((p * (1 - p)) / n))

Upper bound: p + (1.282 * sqrt((p * (1 - p)) / n))Since the value of p is not provided in the question, we cannot determine the specific confidence interval without knowing the sample proportion.(c) To construct a 95% confidence interval about the population proportion (p) when the sample size (n) is 13, we can use the normal distribution approximation. The formula for the confidence interval is:Confidence Interval = p ± (z * sqrt((p * (1 - p)) / n))where p is sample proportion, n is  sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level.From the standard normal distribution, for a 95% confidence level, the critical value is approximately 1.96.

substituting :

Lower bound: p - (1.96 * sqrt((p * (1 - p)) / n))

Upper bound: p + (1.96 * sqrt((p * (1 - p)) / n))

Since the value of p is not provided in the question, we cannot determine the specific confidence interval without knowing the sample proportion.(d) Yes, we could have computed the confidence intervals in parts (a)-(c) even if the population had not been normally distributed. The central limit theorem allows us to use the t-distribution and normal approximation for large sample sizes to construct confidence intervals, regardless of the population's distribution, as long as the sample size is sufficiently large.

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Answer:

The measure of ∠A'B'C' is 125°

Step-by-step explanation:

The given information are;

The measure of ∠ABC = 125°

The transformation applied to ∠ABC = 75° rotation about point B

The vertices of the image formed after rotation = ∠A'B'C'

Therefore, given that a rotational transformation is a form of rigid transformation, we have that the size and shape of the figure in the preimage = The size and shape of the figure of the image

Therefore, the measure of m∠ABC = The measure of m∠A'B'C'.

The measure of the angle  A'B'C' which is created by rotating angle ABC 75° about point B is 125 degrees.

Rotation of a figure is the transformation of it about a point in either clockwise or anticlockwise direction. By rotating, a figure changes the coordinate point of the figure.

The following information regarded to angle ABC are given.

The rotation of 75 degree is applied on the given angle ABC from the point B. This will change the coordinate points of the point A and point C.

As it is known that the rotation changes the coordinate point and the position of the shape but does not change the shape and size of the original figure.

Hence, the measure of the angle  A'B'C' which is created by rotating angle ABC 75° about point B is 125 degrees.

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Answer:

31 cm

Step-by-step explanation:

the scatterplot is rising, so based on an assumption of where a line going through the scatterplot is going to go, you get 41

The object falling from a tower of 1503ft will take 9.69 seconds to reach the ground.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

In the function s(t) = 16t²

The height of the object is at 1503ft, let's substitute this and solve for t

1503 =  16t²

t² = 1503/16

t = 9.69seconds

It will take the object 9.69 seconds to fall from a height of 1503 ft

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Answer:

C. 25 years

Step-by-step explanation:

From my understanding you were asking to;

Double Allan's age, which is three, so double of his age would be six

Subtract Allan's age, three, from George's age, seven, and you would get four

Add George's age, seven, to Juan's age, eight, and get fifteen

Then you asked to add all the results together which would be;

6 + 4 + 15

That would equal 25 and since we were measuring years it would be 25 years, not just 25.

The property illustrated in "√2+√8 is a real number" is the closure property of addition,

The property illustrated in the given statement is the closure property of addition, which states that the sum of two real numbers is also a real number.

The closure property of addition states that the sum of any two real numbers is also a real number. In the given statement, √2 and √8 are both real numbers, and therefore their sum √2+√8 is also a real number.

This property applies to all real numbers, and it is an important property of the number system. which states that the sum of two real numbers is also a real number.

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Answer:  x = 25

. . . . . . . . . . . . . .

Answer:

(2.5, 5.5)

Step-by-step explanation:

The system of equation is not well written

Let the system of equations be;

y = x+3

y = 3x - 2

Equate both expressions to get x;

x + 3 = 3x - 2

x - 3x = -2-3

-2x = -5

x = 5/2

x = 2.5

Get the value of y;

y = x+3

y = 2.5+3

y = 5.5

Hence the required coordinate point is (2.5, 5.5)

Note that the second equation was assumed but the same steps can be taken to solve the given equation

Answer:

-1

Step-by-step explanation:

1) 5=-x+6

2) -x=6-5

3) x=-1

The present value of $2,500 per year for 10 years discounted back to the present at 7 percent is $17,462.03.

To calculate the present value of an ordinary annuity, we can use the formula:

PV = A * [1 - (1 + r)^(-n)] / r,

where PV is the present value, A is the annual payment, r is the discount rate per period, and n is the number of periods.

In this case, the annual payment is $2,500, the discount rate is 7 percent (or 0.07 as a decimal), and the number of periods is 10 years. Plugging in these values into the formula, we can calculate the present value:

PV = $2,500 * [1 - (1 + 0.07)^(-10)] / 0.07 ≈ $17,462.03.

Therefore, the present value of $2,500 per year for 10 years discounted back to the present at 7 percent is approximately $17,462.03. This represents the amount of money needed in the present to be equivalent to receiving $2,500 per year for 10 years with a 7 percent discount rate.

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For the obtuse triangle with 16 and 21 as two sides of the triangle there are 18 possible lengths for the third side

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

With the obtuse triangle we have the following rule:

a^2 + b^2 < c^2

a + b > c

So, lets called the third side (c)

c + 16 > 21 =  c > 5

c+21 > 16 = c > - 5

21 + 16 > c =  37 > c

The third side must be:  5 < c < 37

To be an obtuse triangle we have:

c^2 > 21^2 +16^2

c^2 > 697

c > 26 (positive integer)

Calculating if the other angles are obtuse:

21^2 > c^2 + 16^2

c^2 < 185

c < 14

16^2 > c^2 + 21^2

c^2 < a negative integer, not possible

This means that for the angle opposite the third side to be obtuse should be:

26 < c < 37

27,28,29,30,31,32,33,34,35,36 = 10 possible lengths

And for the angle opposite the side 21 to be obtuse, should be:

5 < c < 14

6,7,8,9,10,11,12,13 = 8 possible lengths

Total possible lengths = 10 + 8 = 18 possible lengths

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Answer: Slope: 0

              y-intercept: (0,7)

Step-by-step explanation:

Answer:

A dilation would make them similar.  Similar is the same shape, but not necessarily the same size.  A dilation is a transformation that can make figures shrink or expand.  The other forms of transformations are rigid. They do not change the size.

Step-by-step explanation:

Answer:

Lets solve = 3/5 ÷ 1/2

3/5 ÷ 1/2

= 3/5 × 2/1

= 3 × 2/5 × 1

= 6/5

In mixed fraction its

\(1 \frac{1}{5} \)

____________________

Now lets solve "a" option

3/5 × 2

= 3 × 2/5 × 1

= 6/5

In mixed fraction

\(1 \frac{1}{5} \)

So option a = 3/5 x 2/1 is ur answer

is \( \sf \frac{3}{2} \times \frac{2}{1} [B]\)

\( \sf \frac{ 3}{5} \div \frac{1}{2} \)

\( \sf = \frac{3}{2} \times \frac{2}{1} [B]\)

Which multiplication expression is equal to 3/5 1/2 the answer is \( \sf \frac{3}{2} \times \frac{2}{1} [B]\).

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

The amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly can be calculated as follows:

Given, Principal = Rs 1200Time = 1.5 yearsInterest rate = 40% per annum, compounded quarterly

Let r be the quarterly rate of interest. Then we can convert the annual interest rate to quarterly interest rate using the following formula: \text{Annual interest rate} = (1 + \text{Quarterly rate})^4 - 1$$

Substituting the values, we get:0.40 = (1 + r)^4 - 1 Solving for r, we get:r = 0.095 or 9.5% per quarter

Now, we can use the formula for the amount of money after time t, compounded quarterly: $A = P \left( 1 + \frac{r}{4} \right)^{4t}

Substituting the values, we get:A = Rs 1200 x $\left(1 + \frac{0.095}{4} \right)^{4 \times 1.5}= Rs 1893.09

Therefore, the amount of the sum Rs 1200 for one and a half year at 40 percent of interest compounded quarterly is Rs 1893.09.

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Answer: A

Step-by-step explanation:

\(\left(\frac{7}{8} \right)\left(-\frac{32}{49} \right)(14)(m^{2}n)(mn^{3})(mn^{2})=\boxed{8m^{4}n^{6}}\)

Answer:

Are m<4 and m<8 supplementary angles? If that's the case, the answer is:

x=178/9

m<4=81 1/9 degrees

m<8=98 8/9 degrees

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

m<4+m<8=180

4x+2+5x=180

9x+2=180

9x=178

x=178/9

m<4=4x+2

m<4=4(178/9)+2*9/9

m<4=712/9 + 18/9

m<4=730/9 degrees

m<4=(729+1)/9

m<4=729/9 + 1/9

m<4=81 1/9 degrees

m<8=5(178/9)

m<8=890/9

m<8=(882+8)/9

m<8=882/9 + 8/9

m<8=98 8/9 degrees

Step-by-step explanation:

"Financial" as it is not an effectiveness MIS metric.

To determine which one is not an effectiveness MIS metric, we need to understand the purpose of these metrics. Effectiveness MIS metrics measure how well a system is achieving its intended goals and objectives.

Customer satisfaction is a common metric used to assess the effectiveness of a system. It measures how satisfied customers are with the product or service provided.

Conversion rates refer to the percentage of website visitors who complete a desired action, such as making a purchase. This metric is often used to assess the effectiveness of marketing efforts.

Financial metrics, such as revenue and profit, are crucial indicators of a system's effectiveness in generating financial returns.

Response time measures the speed at which a system responds to user requests, which is an important metric for evaluating system performance.

Therefore, based on the given options, "Financial" is not a type of effectiveness MIS metric. It is a separate category of metrics that focuses on financial performance rather than the overall effectiveness of a system.

In summary, the answer is "Financial" as it is not an effectiveness MIS metric.

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The the cost of 13 CDs would be $30.

A cost function is a function of input prices and output quantity whose value is the cost of making that output given those input prices, often applied through the use of the cost curve by companies to minimize cost and maximize production efficiency.

If $20 represents the cost of  the 5 used CDs, than your formula would be "20 + 4x" , with x being the amount of extra CDs you purchase.

The number of CDs minus 5 is our x value, because the first 5 are the used CDs bundled into the $20 group. Thus;

26 + 4(13 - 5)

26 + 4(1)

26 + 4 = $30

Thus, we conclude that the cost of 13 CDs would be $30

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Let the blank space be x. So we have the following

The main purpose is to find the value of x by applying mathematical operations on both sides of the equality sign.

First, we add the numbers on the left hand side. So we get

Now, we subtract 2 on both sides, so we get

So, the value of x that makes the equation true is x=10. That is, option C

The side lengths of the right triangle are: shorter leg = 7 cm, longer leg = 24 cm, and hypotenuse = 25 cm.

Let's denote the length of the shorter leg as x.

According to the information:

The length of the longer leg is 3 cm more than three times the length of the shorter leg, which can be expressed as 3x + 3.

The length of the hypotenuse is 4 cm more than three times the length of the shorter leg, which can be expressed as 3x + 4.

In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using this, we can set up the equation:

(x)²+ (3x + 3)² = (3x + 4)²

Expanding and simplifying the equation:

x² + (9x² + 18x + 9) = (9x² + 24x + 16)

Combining like terms:

10x² + 18x + 9 = 9x² + 24x + 16

Moving all terms to one side of the equation:

10x² + 18x + 9 - 9x² - 24x - 16 = 0

Simplifying:

x² - 6x - 7 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have:

(x - 7)(x + 1) = 0

Setting each factor to zero:

x - 7 = 0   or   x + 1 = 0

Solving for x:

x = 7   or   x = -1

Since lengths cannot be negative, we discard the solution x = -1.

Therefore, the length of the shorter leg is x = 7 cm.

Using this value, we can find the length of the longer leg and the hypotenuse:

Length of the longer leg = 3x + 3 = 3(7) + 3 = 21 + 3 = 24 cm

Length of the hypotenuse = 3x + 4 = 3(7) + 4 = 21 + 4 = 25 cm

So, the side lengths of the triangle are:

Shorter leg = 7 cm

Longer leg = 24 cm

Hypotenuse = 25 cm

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Answer:

exponent

Step-by-step explanation:

Answer:

\(\frac{x-1}{x+2}\)

Step-by-step explanation:

simplifying the equation:  \(x^2-3x+2/x^2-1\)

1) Rewrite the equation so it's easier to understand:

\(\frac{x^2-3x+2}{x^2-4}\)

2) factor \(x^2-3x+2\):

\(x^2-3x+2\) \(=> (x-1)(x-2)\)

3) factor \(x^2-4\):

\(x^2-4 => (x+2)(x-2)\)

Meaning: \(\frac{(x-1)(x-2)}{(x+2)(x-2)}\)

4) Cancel the common factor: \((x-2)\) from the numerator and the denominator:

\(=\frac{x-1}{x+2}\)

The statements that is true about the similarity of the two triangles the option D

D. ΔMNO and ΔJKL are not similar triangles

Similar triangles are triangles which have proportional corresponding sides

The parameters in the question are;

The length of segment MN = 20

Length of segment NO = 12

Length of segment OM = 25

Measure of angle ∠O = 56°

Length of segment LJ =- 15

Length of segment JK = 12

Length of segment KL = 9

Measure of angle ∠L = 56°

Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included  angle between the two sides are congruent

The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL

However, the ratio of the sides  LK to ON and JL to MO are;

9/12 ≠ 15/25

Therefore, the triangles are not similar

The correct option is option D

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

yes

Step-by-step explanation:

For the values for a linear relationship given in the tables ,the required equation of line is :

First table : y =2x -1

Second table : y = -4x +1

As given in the question,

Values for a linear relationship

First table :

x :     -2          0          2          4      

y :     -5         -1         3           7

(x₁ , y₁) = (-2 , -5)

(x₂ , y₂) = (0,-1)

Equation of line:

(y -y₁) /(x-x₁) = (y₂ -y₁) /(x₂ -x₁)

⇒ (y+5)/(x+2) = (-1+5)/ (0+2)

⇒ y+5 = 2(x+2)

⇒ y=2x -1

Second table :

x :     -4          -3         -2          -1      

y :     17         13          9           5

(x₁ , y₁) = (-4 , 17)

(x₂ , y₂) = (-3,13)

Equation of line:

(y -y₁) /(x-x₁) = (y₂ -y₁) /(x₂ -x₁)

⇒ (y-17)/(x+4) = (13-17)/ (-3+4)

⇒ y-17 = -4(x+4)

⇒ y=-4x +1

Therefore, for the values for a linear relationship given in the tables ,the required equation of line is :

First table : y =2x -1

Second table : y = -4x +1

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Answer:

Minimize

Step-by-step explanation:

Hope this helps!