Which equation is equivalent to 16^2p = 32^p+3?

Answer:

the answer is A. g(x) = -x^2 - 4

Step-by-step explanation:

hope this helps! :)

Check the picture below.

The volume of the rectangular prism is equal to 8 cubic inches.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

Volume of rectangular prism = L × W × H

Volume of rectangular prism = 2 × 2 × 2

Volume of rectangular prism = 8 in³.

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Missing information:

What is the volume of the rectangular prism shown in the image above?

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features.

When a researcher wants to report the average cost of college tuition from the 1950s until present time, descriptive statistics are the appropriate method to use. Descriptive statistics are used to summarize and describe data, making them useful for providing a clear understanding of a dataset's important features. By using descriptive statistics, the researcher can calculate measures of central tendency, such as the mean, median, and mode, to determine the typical or average cost of college tuition over time. Additionally, measures of variability, such as the range and standard deviation, can be calculated to understand the spread of the data. Descriptive statistics are commonly used in many fields, including business, economics, psychology, and education, and can provide valuable insights into trends, patterns, and distributions within a dataset.

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Answer:

B.

g= 10

Step-by-step explanation:

Answer:

167.67 divided by 8.1 = 20.7

Answer:

children ticket= $15

adult ticket= $18

Step-by-step explanation:

let's take a to represent adults and c to represent children

3a + 4c = 114 [1]

2a + 3c = 81 [2]

multiply the first equation by 2 and the second equation by 3

6a + 8c = 228 [3]

6a + 9c = 243 [4]

subtract [3] from [4] and it would leave you with

-c = -15

c = 15

now, substitute c = 15 into [1](the very first equation)

3a + 4c = 114 [1]

3a + 4(15) = 114

3a = 114 – 4(15)

3a = 54

then divide both sides by 3

a = 18

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

The concept is the Chi-square test, a statistical test for comparing observed results to expected results. The answer is option A.

The test statistic x^2 is equivalent to the test statistic Z. Homogeneity 2x2 The chi-square statistic (and the test) is equivalent to a two proportion test.

The chi-square test is a statistical test used to compare observed results to expected results.The purpose of this test is to determine whether the difference between the observed and expected data is due to chance or to the relationship between the variables being studied. The

Two Ratio Z-Test is a statistical hypothesis test used to determine whether two ratios are different from each other. When you run the test, the z-statistic is calculated from two independent samples, and the null hypothesis is that the two proportions are equal.

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(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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Answer: about 270

Step-by-step explanation:

If you look closely at 200 ml, you will see that there are 5 evenly spaced bars. This tells us that 200-300 ml is split by 20s. Counting the bars, you reach 260, but it goes almost halfway past it. Therefore, we get 270 since 270 is halfway past 260 and 280.

The relative frequencies for this problem are given as follows:

A relative frequency is calculated as the number of desired outcomes divided by the number of total outcomes.

The total number of people is given as follows:

32 + 68 = 100.

Of those, 25 + 45 = 70 wear a watch, hence the relative frequency is given as follows:

70/100 = 0.7.

30 do not wear a watch, hence the relative frequency is given as follows:

30/100 = 0.3.

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The value of the side length x is equal to 14 using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

sin45 = 7√2/x {opposite/hypotenuse}

√2/2 = 7√2/x {sin45 = √2/2}

x = 7√2 × 2/√2 {cross multiplication}

x = 7 × 2

x = 14

Therefore, the value of the side length x is equal to 14 using the trigonometric ratio of sine.

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Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

Answer:Step-by-step explanation:

G(F(x))=(x - 5)²

The correct answer is U - II = I + III + IV.

In order to solve problems based on these sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.

c represent the compliment of the particular state.

U is the union set

∩ represent intersection between the neighbouring sets

Therefore,

Bc = U - B = I + II

Bc∩A = Area common in Bc and A = II

(Bc∩A)c = Area in U but not in (Bc∩A) = U - II = I + III + IV

So, answer is d.

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To describe the temperatures for the week, we can apply the following statistical tools:

a) Find the mean, median, mode, and range.

c) Construct a line graph.

d) Construct a stem and leaf plot.

We can describe temperatures using measures of central tendencies (especially the mean, median, and mode).

The mean temperature is the average, which shows the overall trend in temperature changes.  It is computed by adding up the temperatures for the period and diving by the number of data values.

In addition, the median gives the middle value when the data set is ordered in ascending or descending orders. Similarly, the mode gives the highest temperature occurrence within the period. It may not be useful here.

We can estimate the difference between the highest and lowest temperature for the week with the range.

A line graph (showing connecting lines) and a stem-and-leaf plot (like a bar graph) can graphically describe the temperatures for the week.

Thus, we can use Options A, C, and D to describe the temperature.

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What could you do to describe the following data, showing temperatures for the week? (Check all that apply.)

Mon - 65°

Tues - 67°

Wed - 66°

Thur - 70°

Fri - 72°

Sat - 68°

Sun - 69°

a) Find the mean, median, mode, and range.

b) Survey people about the weather.

c) Construct a line graph.

d) Construct a stem-and-leaf plot.

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Answer:

O a=0

Step-by-step explanation:

a) The equation has a root in the interval (-1,0)

b) The solution of \(2x+3cos(x)+e^{x}=0\) by using the Bisection Method is x=0.9977 accurate within \(10^{-3}\)

a) The intermediate zero theorem (Bolzano's Theorem) tells us that whenever you have a continuous function in a given interval and the extremes of the functions on this interval have oposite signs, then there must be a zero in between those extreme values.

"If a function f on the closed interval [a,b] is a continuous function and it holds that f(a)>0 and f(b)<0 or f(a)<0 and f(b)>0, then there is at least one x-value such that f(x)=0"

So basically we need to evaluate the given equation for both extremes of the interval x=-1 and x=0, if they return results opposite in sign, then there must be a zero in that interval, so let's evaluate the function for x=-1:

\(2x+3cos(x)+e^{x}\)

\(2(-1)+3cos(-1)+e^{-1}=-0.0112\)

Let's now test for x=0

\(2x+3cos(x)+e^{x}\)

\(2(0)+3cos(0)+e^{0}=4\)

So notice we ended up with two values -0.0112 and 4. One is positive and the other is negative, therefore there must be a zero in that interval.

b) The zero is located at x=-0.9977

The idea of the bisection method is to find values for x in the middle of two x-values that return opposite sign answers when evaluated on the given function. So we can start with the extremes of the given interval:

x=-1 and x=0

so we find the value in the middle by using the following formula:

\(mid-value=\frac{x_{1}+x_{2}}{2}\)

so we get:

\(mid-value=\frac{-1+0}{2}\)

mid-value=-0.5

Next, we evaluate the given function for that value:

\(2(-0.5)+3cos(-0.5)+e^{-0.5}=2.2393\)

Since we got a positive answer, we now find the midpoint between -0.5 and -1 (which was the last x-value that returned a negative answer) so we get:

\(mid-value=\frac{-1-0.5}{2}\)

mid-value=-0.75

Next, we evaluate the given function for that value:

\(2(-0.75)+3cos(-0.75)+e^{-0.75}=1.1674\)

and we repeat the process until que get to the desired accuracy. I uploaded a table that has the corresponding iterations and its answers. There were 14 iterations done until we got to the final answer x=-0.9977.

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x | y | 1st difference | 2nd difference

-10 | 200 | |

-9 | 162 | 162-200 = -38 |

-8 | 128 | 128 - 162 = -34 | -34 - (-38) = 4

-7 | 98 | 98 - 128 = -30 | -30 - (-34) = 4

-6 | 72 | 72 - 98 = -26 | -26 - (-30) = 4

Since the first differences all are different, then the function is not linear.

Given that all the second differences are equal, then the function is quadratic.

The function is an exponential growth function

The function is given as

y=2(1.06)^9

We can begin by rewriting the given equation as:

y = 2 * 1.06t

So, we have

y = 2 * (1 + 0.06)^t

Now we can see that the equation is in the form y = a*b^t,

where a = 2 and b = 1.06^9

This equation represents exponential growth because the base of the exponent, b = 1.06, is greater than 1.

We can re-write it in the form y = a(1+r)t,

we can find the value of r by subtracting 1 from 1.06 which is 0.06 and the value of a is 2.

so we have y = 2(1+0.06)^t

So, the equation represents exponential growth with a = 2 and r = 0.06

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Answer:

77.40

Step-by-step explanation:

Answer:

C. 5 inches

Step-by-step explanation:

I’m area you have to multiply L • W

But since we don’t know the width we can divide the length by the area.

40/8 = 5

So the answer would be 5.

Another way to solve this problem is with using guess and check.

I hope it helps! Have a great day!

Anygays~

Answer:

C. 5 inches

Step-by-step explanation:

Use the numbers we have in the word problem, so you´d divide 40 by 8 since you´re trying to find the width. 40 is the area and 8 is the length so divide it tofind the width.

40/8 = 5

ANSWER: 5 inches

I hope it helps! Have a great day!