A baseball is thrown into the air from a height of 5 feet. The ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. Which equation models the height of the baseball? Assume that acceleration due to gravity is –16 ft/s2.

Answer:

The slope of the line would be 1

(4-1)/(6-3)= 1

Answer:

5.1

Step-by-step explanation:

so the leaning ladder makes a right angled triangle so we can use pythagoras to calculate the the length (the hypotenuse):

5²+1²=x²

25+1=x²

√26=x

x=5.099...

and now we round to one d.p so it becomes 5.1 (1 d.p) as the hundreths digit is 9 and 9 is rounded up.

Step-by-step explanation:

90 girls were at the dance

Answer:

60:90

Step-by-step explanation:

use cross multiplication :)))

Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of different sizes.

Frequency distributions can show the actual number of observations falling in each range or the percentage of observations. In the latter sample, the distribution is called a relative frequency distribution.

Frequency distribution tables can be utilised for both categorical and numeric variables. Continuous variables should only be used with class intervals, which will be described shortly.

A relative frequency distribution displays the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.

--This question is incomplete; the complete question is

"Relative frequency distributions are generally more useful than frequency distributions when _____."--

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Answer:

1/12

Step-by-step explanation:

Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

Answer:

The answer is 1.5

3/2=1.5

Answer:

Step-by-step explanation:

1. Finding  \(\overrightarrow{AB}\)  (or \(\overrightarrow{BA}\)):

\(\overrightarrow{AB}=\overrightarrow{OA}-\overrightarrow{OB}= \left[\big5\atop\big3\right]-\left[\big2\atop-\big5\right]= \left[\big5-\big2\atop\big3-(-\big5)\right]=\left[\big3\atop\big8\right]\)

2. Calculating length of  \(\overrightarrow{OA}\,,\ \overrightarrow{OB}\ \text{and}\ \overrightarrow{AB}\):

\(|\overrightarrow{OA}|=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}\approx5.831\\\\ |\overrightarrow{OB}|=\sqrt{2^2+(-5)^2}=\sqrt{4+25}=\sqrt{29}\approx5.385\\\\ |\overrightarrow{AB}|=\sqrt{3^2+8^2}=\sqrt{9+64}=\sqrt{73}\approx8.544\)

3. Calculating perimeter:

\(P=|\overrightarrow{OA}|+|\overrightarrow{OB}|+|\overrightarrow{AB}|=\sqrt{34}+\sqrt{29}+\sqrt{73}\approx5.831+5.385+8.544=19.76\)

The scatterplot is the correct answer.

A scatter plot uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.

The dots in a scatter plot not only report the values of individual data points but also patterns when the data are taken as a whole.

Identification of correlational relationships is common with scatter plots. In these cases, we want to know, if we were given a particular horizontal value, what a good prediction would be for the vertical value.

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Answer:

1 1/8

Step-by-step explanation:

Make this an improper fraction for simplicity: 27/4

now divide into six portions:  (27/4)/6 = (27/6)/4 = 27/24 = 1 3/24 = 1 1/8

Answer:

positive association and linear association

Step-by-step explanation:

Answer:

If Shape C is similar to Shape D, then we know that the ratio of corresponding side lengths is the same. In this case, we can set up the following proportion:

9 / 6 = x / 10

To solve for x, we can cross-multiply and simplify:

9 * 10 = 6 * x

90 = 6x

x = 15

Therefore, the value of x is 15 cm.

Answer:

The answer for x is approximately 5.6

Step-by-step explanation:

9/9.6=x/6

cross multiply

9.6x=9×6

9.6x=54

divide both sides by 9.6

9.6x/9.6=54/9.6

x=5.625

x≈5.6

The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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Answer:

2

Step-by-step explanation:

4*2=8 and 8+4=12

Answer:

1/2 pi

Step by step explanation:

Find the circumference

2πr = 2xπx2 = 4π

Find the angle of JHI

Since 1/2π is 1/8 of 4π,

Angle JHI should also be 1/8 of 360 = 45 degrees

To find area, 45/360 x π X 2^2

= 1/8 x 4π

= 1/2 π

Answer:

D!

Step-by-step explanation:

We need to obviously subtract, only C and D do thatt. But, you don't multiple t or 28 by 4. You need to multiply the difference, so you need parentheses!

The area of the composite figure is the sum of the area of a semicircle, the area of a trapezoid, and the area of two similar rectangles. Then the correct option is D.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Two rectangles, a trapezoid, and a semicircle make form a composite figure.

The diagram of the composite figure is given below.

The area of the composite figure is the sum of the area of a semicircle, the area of a trapezoid, and the area of two similar rectangles. Then the correct option is D.

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Answer:

D

Step-by-step explanation:

Answer:

5-hour reunion at Picnic Place will cost $250.

5-hour reunion at Total Tent will cost $350.

15 hours for both choices to cost the same.

Explanation:

Let x represent the number of hours.

Let y represent the total cost.

For Picnic Place, our equation can be written as;

For a 5-hour reunion at Picnic Place, the charge will be;

For Total Tent, our equation can be written as;

For a 5-hour reunion, the cost will be;

To determine how many hours onwill need to reserve both shelters for both choices to cost the same, we just need to equate both equations and solve for x;

Answer:

r=6.1cm

volume=1/3πr^2

=1/3×22/7×6.1^2

=818.62/21

=38.98cm^3

Answer: y=3x-8, y=5x-8, and y=2x-8

Step-by-step explanation:

These equations are all lines in slope-intercept form (y=mx+b where b is the y-intercept). y=3x-8, y=5x-8, and y=2x-8 all have -8 as the b value. Therefore, these equations have the same y-intercept.

The surveyor, on average, lays out a rectangle whose area is only 1/9 of the area of the square.

Given:X and Y are independent random variables.E(XY) = E(X) . E(Y).

The problem wants us to show that E(XY) = E(X) . E(Y) and apply this result in Exercise 25, where X and Y are independent random variables following uniform distribution in a certain interval.

Proof:Let X and Y be independent random variables, and their joint probability density function (PDF) be f(x, y).

Now, E(XY) can be expressed as follows:E(XY) = ∫∫ xy f(x, y) dxdy [double integral of xy f(x, y) w.r.t x and y]

By definition, E(X) = ∫∫ x fX(x) dxand E(Y) = ∫∫ y fY(y) dy

By definition of independence of X and Y, their joint PDF is equal to the product of their marginal PDFs, i.e., f(x, y) = fX(x) . fY (y).

Therefore, E(XY) can also be expressed as:E(XY) = ∫∫ xy fX(x) . fY(y) dxdy = ∫∫ x fX(x) dx ∫∫ y fY(y) dy = E(X) . E(Y)

Thus, E(XY) = E(X) . E(Y) when X and Y are independent random variables.

Suppose X and Y are independent random variables, each uniformly distributed on the interval [L-A, L+A], where 0< A < L.

And, the surveyor wants to lay out a square region with each side having length L but instead lays out a rectangle in which the north–south sides both have length X and the east–west sides both have length Y.

Now, we need to show that the expected value of the area of the rectangle that the surveyor lays out is L^2.The area of the rectangle is given by XY.

Hence, the expected value of the area of the rectangle is: E(XY) = E(X) . E(Y) (from the above proof)E(X) = E(Y) = L2 ∫ (L-A) to (L+A) dx / 2A= L2 ∫ (0) to (2A) dx / 2A= L^2 / 3

Hence, E(XY) = E(X) . E(Y) = L^2 / 9.

But, the expected value of the area of the square is L^2.

Hence, the surveyor, on average, lays out a rectangle whose area is only 1/9 of the area of the square.

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Answer:

0

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

1 + 1/0 = x

-1  

1/0 = x

x0

1 = x

Backwards PEMDAS where each thing you do backwards cancles itself out.

Answer:

52feet

Step-by-step explanation:

The set up will be a right angle

Let the angle of depression be 30°

The height above the sea level will be the opposite

The distance of the ship from the base is x (adjacent)

Using TOA

Tan theta = opposite/adjacent

Tan 30 = 30/x

x = 30/tan 30

x = 30/0.5774

x = 51.96

x ≈ 52 feet to the nearest foot

Answer:

Step-by-step explanation:

Tanisha, Elicia, and Ajua are cousins. Tanisha is twice as old as Ajua, and Elicia is two years older than Tanisha. The sum of all their ages is 37. Use variable expressions and calculate the age of each girl

Let us represent:

The age of :

Tanisha = a

Elicia = b

Ajua = c

Tanisha, Elicia, and Ajua are cousins. Tanisha is twice as old as Ajua

a = 2c

c = 2/a

Elicia is two years older than Tanisha.l

b = a + 2

The sum of all their ages is 37.

a + b + c = 37

We substitute

a + a + 2 + 2/a = 37

2a + 2 + 2/a = 37

Use variable expressions and calculate the age of each girl

The number positioned at point A is -4.25.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to compare two numbers such as 4 and 1. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

In this scenario, the given number line uses a scale of 1:0.25. Therefore, the number (numerical value) that is placed at point A is given by:

Point A = -4.5 - 0.25

Point A = -4.25.

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The absolute value of the difference between the point estimate and the population parameter it estimates is sampling error.

The number's absolute value, which ignores orientation, indicates how far it is from zero on the number line. A number can never be negative in absolute terms.

Concepts which are used in the given problems:

The incorrect options can be found below:

Because the precision is the estimate that is near from the various samples, the absolute magnitude of the difference between the point estimate and the population parameter would not be a precision. Additionally, it is not a standard error since a standard error is an error that is far beyond the range of the sample mean. However, it is not a confidence error since a confidence error is a measure of how far the findings would deviate from the population under consideration.

By using the  concept of precision, standard error and error of confidence, the incorrect choices are discovered.

The correct choice may be found below:

Sampling error is the measurement of the distance or difference between the population parameter and the sample's point estimate. The sampling mistake is an inaccuracy that results from drawing conclusions about the sample rather than the population being studied.

The idea of sampling error is used to calculate the absolute value of the distinction between both the point estimate and the population parameter is predicts.

Thus, the absolute value of the difference between the point estimate and the population parameter it estimates is sampling error.

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The MMPI-2 test is used for the assessment of psychopathology and personality of patients.

It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.

A score of 30 or less is usually considered very low.

The questions are answered by the patient, usually in a clinical or research setting.

A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.

The following are the parameters of the one-sample t-test:Groups:

18 participants

Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30

Type of test: One-tailed test

Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.

Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734

Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5

If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).

For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13

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Answer:

We. can see there's a  black point at -3.7 and an arrow going to the left.

As the arrow goes to the left, it must be less than -3.7 or less than or equal to -3.7, now, we will need to see the colour of the point to know which it is.

As there is a black point, -3.7 is also contained in this range...

What does that mean? That means it will be less than or equal to -3.7

So we know the correct option is a) less than or equal to -3.7, what we could write as (\(-\infty,-3.7\)].

The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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