Write a compound inequality that represents the following phrase. Graph the solutions.
all real numbers that are between -7 and 5, inclusive

Answer:

Let's assume that the distance between Chicago and Hoopertown is represented by 'x' miles.

According to the given information:

Raymond lives 23 miles from Chicago, so the distance between Amanda and Chicago is 23 - 15 = 8 miles.

Since Amanda lives halfway between Charlie and Chicago, the distance between Charlie and Chicago is also 8 miles.

Therefore, the distance between Charlie and Hoopertown is x - 8 miles.

Since Charlie lives halfway between Chicago and Hoopertown, the distance between Raymond and Charlie is (x - 8) / 2 miles.

Given that Raymond lives 15 miles from Amanda, we can set up the following equation:

(x - 8) / 2 = 15

To solve for x, we can multiply both sides of the equation by 2:

x - 8 = 30

Next, we can isolate x by adding 8 to both sides of the equation:

x = 38

Step-by-step explanation:

Hola! Yo te puedo ayudar, pero no se como explicarlo en español muy bien, perdon en avance!

1) 5×10^3+6×10^2

  (5×1000)+(6×100)

   5000+600= 5,600

2a) 3×10^3×1.5×10^8

     (3×1000)×(1.5×10000000)

      3000×150000000= 450,000,000,000

2b) 4.2×10^3×2×10^-7

     (4.2×1000)×(2×0.0000001)

      4200×0.0000002= 0.00084

3a) \(\frac{6*10^5}{3*10^2}\)

    \(\frac{600,000}{300}\) = 2,000

3b) \(\frac{8*10^{-7} }{2*10^{-9} }\)

     \(\frac{0.0000008}{0.000000002}\) = 0.0000000000000016 o 1.6×10-10

4a) (2×10^5)^3

      200000^3= 8,000,000,000,000,000 o 8e+15

4b) (3×10^-12)^2

0.000000000003^2= 0.000000000000000000000006 o 9e-24

Answer:

it's about 106.71ft

Step-by-step explanation:

make this problem a triangle. the ramp length is 312ft, and it is the hypotenuse of the triangle. 20 is the angle between the ramp and the floor. so what I did was take the sine of 20 and get: sin(20)=x/312 then you multiply both sides by 312 to isolate the variable. multiplying sin(20) by 312 gave me 106.71 + some change idk if you're supposed to round it or not haha.

Answer:

C. dams, bridges, rock quarries, oil wells

Answer:

C

Step-by-step explanation:

he is right above me

the probability that a randomly selected passenger car gets more than 35 mpg is approximately 0.3665.

the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg is approximately 0.087

the probability that all of the passenger cars get more than 35 mpg is approximately 0.015.

We need to find \(P(X > 35),\) where X is the mpg rating of a randomly selected passenger car.

The standard normal distribution and Table 1, we have:

\(z = (35 - 33.8) / 3.5 = 0.34\)

\(P(X > 35) = P(Z > 0.34) = 0.3665\)

\(P(\bar X > 35)\), were \(\bar X\) is the sample mean mpg rating of four randomly selected passenger cars.

The population standard deviation, we use the t-distribution with \(n-1\) degrees of freedom (were \(n = 4\)) and Table 1. We have:

\(t = (35 - 33.8) / (3.5 / \sqrt(4)) = 1.83\)

Using Table 1 with 3 degrees of freedom (\(n-1 = 4-1\)), we find:

\(P(T > 1.83) = 0.087\)

We need to find \(P(X1 > 35\) and \(X2 > 35\) and \(X3 > 35\) and \(X4 > 35\)), where X1, X2, X3, and X4 are the mpg ratings of four randomly selected passenger cars.

Since the mpg ratings of the four cars are independent and identically distributed, we have:

\(P(X1 > 35\)and\(X2 > 35\) and \(X3 > 35\) and \(X4 > 35\)) =\(P(X > 35)^4\)

From part (a), we know that\(P(X > 35) = 0.3665.\)

\(P(X1 > 35\)and \(X2 > 35\) and\(X3 > 35\) and \(X4 > 35) = 0.3665^4 \approx 0.015\)

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The chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of n=25 is c. 36.415

What is chi-square?

Chi-square (χ²) is a statistical test that measures the relationship between categorical variables. It is used to determine if there is a significant association or independence between two variables based on observed frequencies compared to expected frequencies. The chi-square test is a statistical method used to determine if there is a significant association or independence between categorical variables based on observed and expected frequencies in a contingency table.

Degrees of freedom = n - 1

= 25 - 1

= 24

and alpha = 0.05

χ²⁽⁰°⁰⁵,²⁴⁾ =  36.415      …using chi-square table for right tail.

Therefore, the chi-square value for a one-tailed (upper tail) hypothesis test at a 5% level of significance and a sample size of n=25 is c. 36.415.

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The expression that represents the depth reached by the sea lion, relative to the sea level is the option;

An expression consists of a combination of variables and numbers that are arranged according to the rules with which the operators joining the variables and numbers operate.

The depth reached by the seal = 25 feet

The depth of the seal in relation to the sea level = -25 feet

The depth reached by the sea lion to catch a larger fish = 10 feet less than three times as deep as the seal.

Three times as deep as reached by the seal = 3 × -25 = -75 feet

10 feet less than three times as deep as reached by the seal = -75 feet + 10 feet = -65 feet

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Answer:

i) 4620

ii) 756

Note: to check whether answer is correct, take LCM of answer.

e.g. the answer for the first part is 4620, so once you take LCM of that, the answer should be 3³ × 7 × 2² in its index notation.

Step-by-step explanation:

840 = 2³ × 3 × 5 × 7. 8316 = 2² × 3³ × × 7 × 11

840 = 2³ × 3 × 5 × 7

8316 = 2² × 3³ × × 7 × 11

i) The greatest while number that will divide both 840 and 8316 exactly.

Ans: 2² × 3 × 5 × 7 × 11

= 4620

ii) The smallest whole number that is divisible by both 840 and 8316.

Ans: 2² × 3³ × 7

= 756

HOPE THIS HELPS. TAKE CARE! BYE

The confidence interval for the population proportion p is (0.0346, 0.3132).

The given data is as follows:

Grades Male Female Total

A 14 3 17

B 17 4 21

C 7 16 23

Total 38 23 61

Let p represent the population proportion of all female students who received a grade of B on this test. We need to use a 99% confidence interval to estimate p to four decimal places if possible.

The 99% level of confidence is equivalent to α = 1 - 0.99 = 0.01. The significance level is α = 0.01.

The sample proportion of female students who received a grade of B is:

\(�^=\)

Number of female students who received a grade of B

Total number of female students

=

4

23

=

0.1739

p

^

​

=

Total number of female students

Number of female students who received a grade of B

​

=

23

4

​

=0.1739

The formula to find the confidence interval of the proportion is given by:

\(�^−��/2�^(1−�^)�<�<�^+��/2�^(1−�^)�p^​ −z α/2​  np^​ (1− p^​ )​ ​ <p< p^​ +z α/2​  np^​ (1− p^​ )​ ​\)

Substituting the given values in the above formula:

0.1739

\(−��/20.1739(1−0.1739)23<�<0.1739+��/20.1739(1−0.1739)230.1739−z α/2​  230.1739(1−0.1739)​ ​ <p<0.1739+z α/2​  230.1739(1−0.1739)​\)

​

The value of zα/2 can be obtained from the standard normal distribution table. As this is a two-tailed test, we need to split the 1% area between the two tails. Therefore, the area in one tail is 0.005. This gives z0.005 = 2.58.

Substituting zα/2 = 2.58, n = 23, and $\hat{p}$ = 0.1739 in the above equation to find the confidence interval of p:

0.1739

−

2.58

0.1739

(

1

−

0.1739

)

23

<

�

<

0.1739

+

2.58

0.1739

(

1

−

0.1739

)

23

0.1739−2.58

23

0.1739(1−0.1739)

​

​

<p<0.1739+2.58

23

0.1739(1−0.1739)

​

​

0.0346

<

�

<

0.3132

0.0346<p<0.3132

Hence, the confidence interval for the population proportion p of all female students who received a grade of B on this test is (0.0346, 0.3132) to four decimal places.

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The value of g(-2) is 0 and the value of g(4) is -4.

The function g is defined as a piecewise function that assigns a specific value to the input x depending on the range of x.

For x between -8 and -2 (not including -2) the function g assigns 6 as the output, for x between -2 and 4 (not including 4) the function g assigns 0 as the output, and for x between 4 and 10 (not including 10) the function g assigns -4 as the output. Therefore, for input x = -2, the function g assigns 0 as the output and for input x = 4, the function g assigns -4 as the output.

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Complete question :

consider a function g.

given

g(x) = 6    if  -8 ≤ x < -2

g(x) = 0     if  -2 ≤ x < 4

g(x) = -4     if  -4 ≤ x < 10

find the value of g(-2) and g(4)

Answer:

25.35

Step-by-step explanation:

Area of the shaded portion = Area of semicircle - Area of the right triangle

Area of semicircle = πr²/2

Area of semicircle = 3.14(6)²/2

Area of semicircle = 3.14 * 18

Area of semicircle = 56.52

Area of triangle = 1/2 * base * height

Get the height using the SOH CAH TOA identity

sin 60 = H/12

H = 12sin60

H = 12(0.8660)

H = 10.39

Get the base

12² = b²+10.39²

144 = b²+108

b² = 144 - 108

b² = 36

b = 6

Area of triangle = 1/2 * 6 * 10.39

Area of triangle = 3 * 10.39

Area of triangle = 31.17

Area of shaded portion = 56.52 - 31.17

Area of shaded portion = 25.35

(i) The marginal propensity to consume (MPC) is 0.8.

(ii) The marginal propensity to save (MPS) is 0.2.

(iii) The level of consumption is $360.

(iv) The average propensity to consume (APC) is 0.9 or 90%.

(v) The level of savings is $40.

The given linear equation for consumption, C = $40 + 0.8Y, and the income (Y) is $400, let's calculate the following:

(i) The marginal propensity to consume (MPC):

The marginal propensity to consume represents the change in consumption resulting from a change in income. It is the coefficient of the income term in the consumption function.

MPC = ∆C / ∆Y = 0.8

(ii) The marginal propensity to save (MPS):

The marginal propensity to save represents the change in savings resulting from a change in income. It is equal to 1 minus the marginal propensity to consume.

MPS = 1 - MPC = 1 - 0.8 = 0.2

(iii) The level of consumption when income (Y) is $400:

Plug the given income value into the consumption function.

C = $40 + 0.8Y = $40 + 0.8 * $400 = $40 + $320 = $360

Therefore, the level of consumption when income is $400 is $360.

(iv) The average propensity to consume (APC):

The average propensity to consume represents the proportion of income that is spent on consumption. It is calculated by dividing consumption by income.

APC = C / Y = $360 / $400 = 0.9

Therefore, the average propensity to consume is 0.9 or 90%.

(v) The level of savings:

Savings (S) is the difference between income (Y) and consumption (C).

S = Y - C = $400 - $360 = $40

Therefore, the level of savings is $40.

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Answer:

Step-by-step explanation:

rise/run. up 3 and over 4. so your slope is 3/4

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

Explanation:

I'll use the substitution method.

Let's solve the second equation for x.

2y - x = -19

-x = -19-2y

x = 19+2y

Then plug that into the first equation

3x + 4y = -23

3( x ) + 4y = -23

3(19+2y)+4y = -23

3*19 + 3*2y + 4y = -23

57+6y+4y = -23

57+10y = -23

10y = -23-57

10y = -80

y = -80/10

y = -8

Use this y value to find x.

x = 19+2y

x = 19+2(-8)

x = 19-16

x = 3

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

Summary:

We found that x = 3 and y = -8

The ordered pair solution is therefore (x,y) = (3, -8)

Technically you could have stopped once reaching y = -8, since choice B is the only one that fits the description. But it helps to have practice.

Answer:

answer is B

Step-by-step explanation:

picture is upside down.

Answer:

32x - 5y

Step-by-step explanation:

27x - 5y + 5x = 32x - 5y

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

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Answer:

±1/4, ±5/4 (If you could mark as brainliest that would be great!)

Step-by-step explanation:

The possible rational roots of H(x) can be found using the Rational Root Theorem, which states that any rational root of a polynomial must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is 5 and the leading coefficient is 4, so the possible rational roots are:

±1/4, ±5/4

These are the factors of 5 divided by the factors of 4. However, it's important to note that not all of these possible roots will necessarily be actual roots of the polynomial.

Yes, All three interior angles of an acute triangle measure less than 90°. The sum of the angles of an acute triangle adds up to 180°.

An acute triangle is a triangle in which all three interior angles are less than 90º. Although the three interior angles of the acute triangle lie between 0° to 90°, their sum is always 180 degrees.

Triangles can be categorised on the basis of angles and sides. An acute triangle is one that is categorised on the basis of the measurement of angles. If all the interior angles of a triangle are less than 90°, then the triangle is stated to be an acute triangle.

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The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

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Answer:

c

Step-by-step explanation:

c

Answer:

6 and 5

Step-by-step explanation:

angles are a linear pair of supplementary angles, if they are directly neighboring, are created by 2 intersecting lines, and sum up to 180°.

the only 2 angles fulfilling all these criteria are 6 and 5.

Step-by-step explanation:

The shaded area shows the region where it is enclosed in sample space S but does not include the subset B.

Hence it is the complement of B. (A)

If event B is a subset of the sample space S, hence the area represented by the shaded part is complement of B

The set is a collection of members and things.

According to the venn diagram given, the whole set including the set B is the universal set.

The part not shaded is not part of the universal set, hence, we name them the complement of a set.

If event B is a subset of the sample space S, hence the area represented by the shaded part is complement of B

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Answer:

205%

Step-by-step explanation:

Percent means out of 100, so we want to get the denominator as 100

41/20 * 5/5

205/100

The percent is 205

205%

Answer:

u know area of rectangle is length × breadth

therefore, area = (3x+4)×(7x-2)

= 21x²-6x+28x-8

= 21x²+22x-8

= d ans

Answer:

320

Step-by-step explanation:

The top and bottom parts have side lengths of 7 and 4

so 7*4= 28

and there are two of those so 28*2=56

two of the side pieces will have side lengths of 7 and 12

so 7*12=84

and there are two of those so 84*2= 168

and the last set of sides have side lengths of 4 and 12

so 4*12=48

and there are two of those so 48*2=96

now add them all up 56+168+96=320

Answer:

0.37 dinar/dollar

Step-by-step explanation:

To find the exchange rate between dollars and dinar, we can use the formula:

Exchange rate = Amount in dinar / Amount in dollars

First, we need to convert the amount of dollars to dinar using the given exchange rate:

66.60 dinar / 180 dollars = 0.37 dinar/dollar

Therefore, the exchange rate is 0.37 dinar/dollar. This means that for every dollar exchanged, you would receive 0.37 dinar.

When using the least-squares line for prediction, the results are generally more reliable for interpolation rather than extrapolation. Interpolation refers to predicting values within the range of the data used to create the least-squares line, while extrapolation involves predicting values beyond that range. The reliability of extrapolation decreases because it assumes that the relationship between the variables continues outside the observed data, which may not always be accurate due to potential unforeseen factors or changes in the underlying relationship.

The least-squares line is a method used to find the best-fit line that minimizes the sum of the squared residuals between the observed data points and the predicted values on the line. It is commonly used for linear regression analysis to make predictions based on the relationship between two variables.

When using the least-squares line for interpolation, the predicted values are within the range of the data used to create the line. In this scenario, the least-squares line provides a reliable estimate because it is based on observed data points and their relationship. Interpolation assumes that the underlying relationship between the variables remains relatively consistent within the observed range.

However, when it comes to extrapolation, the reliability of the results decreases. Extrapolation involves predicting values beyond the observed range of the data. While it is possible to extend the least-squares line to make predictions, it assumes that the relationship between the variables continues in the same manner outside the observed range. This assumption may not always hold true due to potential unforeseen factors or changes in the relationship between the variables.

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Katie outscored approximately 1.39% of the students in her section.

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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Answer:

.....how when the dimensions are not even clear lol

Answer:

48 cm³

Step-by-step explanation:

the volume of a rectangular prism= length × breadth × height

= 8× 3 × 2

= 48 cm³