The function h(t) = -4.9t2 + h0 gives the height (h), in meters, of an object t seconds after it falls from an initial height (h0). The table shows data for a pebble that fell from a cliff. Image description Choose the quadratic equation that models the situation.

Answer:

yes it is a rational number.

Step-by-step explanation:

Answer:

122.21

Step-by-step explanation:

So our orginal value is 101 dollars,

Markup is increase in value.

The markup in this problem is 21%

We can thikn of this as 121%.

So to find the markup price, we must multiply 121% by 101.

We can thibk of 121% being myltiplying by 101 as:

1.21*101

This will get you:

122.21

So this is your answer!

Hope this helps! :)

Answer:

y=4x

Step-by-step explanation:

Rise= 8

Run= 2

8/2 = 4/1 = 4

y=(slope)x+(y intercept)

y=4x+0

y=4x

y=4x

Answer:

50 items were sold for $75

35 items were sold for $90

Step-by-step explanation:

75 x 50 = 3750

90 x 35 = 3150

3750 +3150 = 6,900

Answer:

C

Step-by-step explanation:

You multiply times 10

Answer:

Length is 13 and width is 3

Step-by-step explanation:

First find an equation that represents this situation.

39 = w * (5w-2)

This works because 39 (the total area) is w (the width) times 5w - 2 (the length). So solve for w.

39 = w * (5w-2)

First, distribute the w over the terms in parentheses

39 = 5w^2 - 2w

Then, subtract (5w^2 - 2w) from both sides.

39 - 5w^2 - 2w = 0

Factor the left side of the equation:

(−5w−13)(w−3)=0

Then set each factor equal to zero.

−5w−13 = 0

Add 13 to both sides, then divide both sides by -5 to isolate w. This leaves you with w = -13/5

Then the other factor:

w−3 = 0

Add 3 to both sides. You're left with w = 3.

So w is either -13/5, or 3. And since the width can't be negative, it is 3.

Now to find the height, plug 3 into the equation we had from earlier:

39 = w * (5w-2)

Substitute w into the equation:

39 = (3) * (5(3)-2)

39 = 3 * (15 - 2)

39 = 3 * (13)

Because 3 * 13 is equal, 13 is the length.

Answer:

6/8 =1.3333... or 33.3%

Step-by-step explanation:

Answer:

33.4 %

Is what I think I am not very sure but try it out hope this helped!

For the given value of domain and range , By observing the figure, The correct answer are options B,C and E.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.

domain : (x | x  3/2)

range : (-∞ , 2)

For these values, Option B , C and E holds that they exists when x  3/2 and it's output that is y exists between  (-∞ , 2).

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Answer:

Heat the solution, dissolve the solute, and let the solution cool verifying nothing settled....(B)

Step-by-step explanation:

hope this helps

Gunther  could dissolve the remaining 6g by heating the solution to dissolve the solute, and let the solution cool verifying nothing settled out.

Solubility of a substance refers to the amount of the substance that dissolves in a given amount of water. The most important factor that affects solubility is the temperature of the system. When the temperature is increased, more solute can be dissolved in the solvent.

Since Gunther needs to add 40 g of a solute to 100 g of water but only 34 grams were added before the solute settled out at room temperature. He could dissolve the remaining 6g by heating the solution to dissolve the solute, and let the solution cool verifying nothing settled out.

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Answer:

17.8

Step-by-step explanation:

Distance Formula: [tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

then plug it in

[tex]d=\sqrt{(10+4)^2+(-3-8)^2}[/tex]

then solve inside the parentheses

[tex]d=\sqrt{(14)^2+(-11)^2}[/tex]

then simplify

[tex]d=\sqrt{196+121}[/tex]

keep simplifying

[tex]d= \sqrt{317}[/tex]

solve the square root

[tex]d=17.80449381[/tex]

round

[tex]d=17.8[/tex]

Answer:

4|x|y²√(3yz)

She forgot the absolute value sign on x, and she left out the exponent on y.

Step-by-step explanation:

Step 1 is correct.

x may be positive, zero, or negative.

√x is always non-negative. To assure that √x² is non-negative, √x² = |x|.

√16 = 4

√3 = √3

√x² = |x|

√y² × √y² = √y^4 = y²

Since y² is always non-negative, there is no need for absolute value sign.

√y^4 = y²

Answer should be

4|x|y²√(3yz)

The graph representing the solution will be of the form a line tending towards left from the point -7/22.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Here the given inequality is less than inequality.

1/7 m < -1/22

Dividing both sides by 1/7, we get,

m < -1/22 ÷ 1/7

m < -1/22 × 7/1

m < -7/22

Hence the graph of the solution will be of the form a straight line tending leftwards from -7/22.

Hence the graph of the given inequality is a straight line tending leftwards from -7/22.

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Answer:

6, 4

Step-by-step explanation:

W to X : 7 - 1 = 6

W to Z : (-2) - (-6) = 4

Answer:

6,4

Step-by-step explanation:

One way is to calculate the distance between W and X, and X and Y to find the length and width.

The distance formula: [tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

plug W(1,-2) and X(7,-2) in to get the length

[tex]\sqrt{(1-7)^2+(-2-(-2))^2}=\sqrt{(-6)^2 +0^2}=\sqrt{36} =6[/tex]

plug X(7,-2) and Y(7,-6) to get the width

[tex]\sqrt{(7-7)^2+(-2-(-6))^2}=\sqrt{0^2 +4^2}=\sqrt{16} =4[/tex]

Step-by-step explanation:

angle 1=68°

angle 3 = 68°

angle 2= 180-68= 112°

angle 4 = 180-68= 112°

Answer: B

Begin by simplifying the given equation, so it's rearranged into standard form. Move all the terms onto one side, so they equal 0. This would result with [tex]4x^{2}[/tex]-3x-9=0. Quadratic formula is (-b±√(b²-4ac))/(2a). Standard form follow this variable format: [tex]ax^{2}[/tex]+bx+c. Use the numbers that correspond with each variable to substitute them into the quadratic formula. This would be

(-(-3)±√(-3²-4(4)(-9)/2(4).

Answer:

H is the answer because 15/32 is the largest so it is in the back

Answer:

J. [tex]\frac{9}{32}, \frac{5}{16},\frac{3}{8},\frac{7}{16},\frac{15}{32},\frac{1}{2}[/tex]

Step-by-step explanation:

7/16 = .4375

1/2 = .5

3/8 = .375

9/32 = .28125

5/16 = .3125

15/32 = .46875

Answer:

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

Given lines:

Plot both of the lines using the graphing calculator by adding the equations, then find the graphical solution as the intersection of the lines.

See attached.

The solution is (-1, 0).

The image for P(9, 1.5) after Translation is P'( 12, 1).

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

P(9, 1.5) with Translating Vector (3, -0.5).

So, Applying the Translation we get

P(9 + 3, 1.5 + (-0.5))

= P(12 , 1.5- 0.5)

= P(12, 1)

hence, the image is P'( 12, 1).

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Answer:

[tex] \sqrt{39} [/tex]

Step-by-step explanation:

5

[tex]5 {}^{2} + x {}^{2} = 8 {}^{2} \\ 25 + x {}^{2} = 64 \\ x {}^{2} = 64 - 25 \\ x {}^{2} = 39 \\ x = \sqrt{39} [/tex]

The length of the unknown length is √39 ft if the other lengths are 5 ft and 8 ft in the right angle triangle.

It is defined as a triangle in which one angle is 90 degrees and the other two angles are acute angles. In a right-angled triangle, the name of the sides are hypotenuse, perpendicular, and base.

Let's suppose the unknown length is x ft

From the Pythagoras theorem:

[tex]\rm hypotenuse^2= perpendicular^2+ base^2[/tex]

[tex]8^2 = 5^2 +x^2[/tex]

64 = 25 + x²

x = √39 ft

Thus, the length of the unknown length is √39 ft if the other lengths are 5 ft and 8 ft in the right angle triangle.

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Answer:

b. Conclude that the mean attendance differs since the p-value = 0.0134 < 0.05.

Step-by-step explanation:

Before testing, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Samples of 31 weeks. The mean attendance on Tuesday evening is calculated as 5,060, with a population standard deviation of 540.

This means that:

[tex]\mu_{T} = 5060, s_T = \frac{540}{\sqrt{31}} = 97[/tex]

The mean attendance on Wednesday evening is calculated as 5,390, with standard deviation of 480.

This means that:

[tex]\mu_{W} = 5390, s_W = \frac{480}{\sqrt{31}} = 86.21[/tex]

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening.

At the null hypothesis we test if there is no difference, that is:

[tex]H_0: \mu_T - \mu_W = 0[/tex]

At the alternate hypothesis, we test if there is difference, that is:

[tex]H_a: \mu_T - \mu_W \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples collected:

[tex]X = \mu_T - \mu_W = 5060 - 5390 = -330[/tex]

[tex]s = \sqrt{s_T^2+s_W^2} = \sqrt{97^2+86.21^2} = 129.77[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-330 - 0}{129.77}[/tex]

[tex]z = -2.54[/tex]

Pvalue of test and decision:

The pvalue of the test is finding the probability of the sample mean difference differing by 0 by at least 330, that is, P(|z| > 2.54), which is 2 multiplied by the pvalue of z = -2.54.

Looking at the z-table, z = -2.54 has a pvalue of 0.0067.

2*0.0067 = 0.0134

The pvalue of the test is 0.0134 < 0.05, which means that there is evidence that the mean attendance differs. The correct answer is given by option b.

From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))

We are given the engineers formula as;

F = (¹¹/₃₀₀)d(F - 13)

Where;

F is the strength of the steel in kilopound per square inch.

d is the diameter of the rocker in millimeters.

From the given formula, we can start by;

Multiply both sides by 300 to get;

300F = 11d(F - 13)

Divide both sides by 11(F - 13) to get;

d = 300F/(11(F - 13))

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The complete table of values of the function is

x    0    1    2    3

y     0   2   5   10

From the question, we have the following parameters that can be used in our computation:

The equation of the function is given as

y = x² + 1

The above function is a quadratic function

This is so because it has the following representation

y = ax² + bx + c

When this function is compared to the equation y = x² + 1, we have the following notations

a = 1

b = 0

c = 1

From the incomplete table of values, we have the x values to be

x = 1, 2, 3

Substitute x = 1, 2, 3 in the equation y = x² + 1

So, we have

When x = 1, y = (1)² + 1 = 2

When x = 2, y = (2)² + 1 = 5

When x = 3, y = (3)² + 1 = 10

When these values are represented on a table, we have

x    0    1    2    3

y     0   2   5   10

The above represents the complete table

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Complete question

Complete table with the Y-values for the equation y=ײ+1

x    0    1    2    3

y     0

Answer:

Thank you for the points...

Step-by-step explanation:

Answer:

a. y = 27.5 - 0.3X

b. 20

Step-by-step explanation:

y =  a + bX

usin the table in the attachment i added, we so for the regression equaion

n = 8

∑xy = 4460

∑x = 280

∑y = 136

∑x²= 10800

[tex]b=\frac{8(4460)-(280)(136)}{8(10800)-280^{2} } \\b=\frac{35680-38080}{86400-78400} \\b=\frac{-2400}{8000} \\b = -0.3[/tex]

from here we solve for a

[tex]a= \frac{136-(-0.3)(280)}{8} \\a =\frac{136+84}{8} \\a=\frac{220}{8} \\a = 27.5[/tex]

a. the estimated regression equation

y = 27.5 - 0.3X

b. at x = 25

y = 27.5 - 0.3(25)

y = 20 is the number of defective parts.

(b) one-sample t-test for a population mean

ur welcome :D

The most appropriate test to be used here would be a b. A one-sample t-test for a population mean.

One sample t-test is used when one wants to compare the mean of a population to another mean for statistical difference which is what the researchers hope to do here in comparing the mean battery life of a new battery to an old one.

A population mean will also be used because the population standard deviation is not given.

In conclusion, option B is correct.

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well, we know that 37.5% have finished it, that leaves unaccounted for 100% - 37.5% = 62.5%.

now, of those 62.5% fellows only 40% have finished only half of it, how many are those?

well, what's 62.5% of 32?   what's 40% of that much?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{62.5\% of 32}}{\left( \cfrac{62.5}{100} \right)32}\implies 20 ~\hfill \stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies \text{\LARGE 8}[/tex]

A) Total mass of 3500 books is 2,800 kilograms.

B) The average mass of one apple is 130 grams.

A) To find the total mass of 3500 books, each with a mass of 800 grams, we can multiply the number of books by the mass of each book:

Total mass = (3500 books) * (800 grams/book)

= 2,800,000 grams

= 2,800 kilograms

Therefore, the Total mass of 3500 books is 2,800 kilograms.

B) To find the average mass of one apple, we can divide the total mass of the apples by the number of apples:

Average mass = (1.04 tonnes) / (8000 apples)

= 130 grams/apple

Therefore, the average mass of one apple is 130 grams.

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Answer:

Step-by-step explanation:

Answer:

J = 33

Step-by-step explanation:

43 - 2k = 33

43 - 10 = 33

33 = 33