Find the volume of the triangular pyramid below. Round your answer to the nearest tenth if necessary.

The correct null hypothesis for this question is H0 : μ = 48° and H1 : μ ≠ 48°

What is null hypothesis ?

In statistical hypothesis testing, the null hypothesis (H0) is a statement that there is no significant difference between a specified population parameter (such as μ) and a hypothesized value (such as 48° F in this case).

The alternative hypothesis (H1), on the other hand, is a statement that there is a significant difference between the population parameter and the hypothesized value. For this particular scenario, the null hypothesis is H0 : μ = 48° F, which means that the refrigerators are maintaining the true mean temperature of 48° F as they are supposed to. The alternative hypothesis is H1 : μ ≠ 48° F, which means that the refrigerators are not maintaining the true mean temperature of 48° F, as claimed by the owner of the brewery.

To test these hypotheses, a sample of refrigerator systems can be taken and their mean temperature can be calculated. If the sample mean is significantly different from 48° F, then the null hypothesis can be rejected in favor of the alternative hypothesis, indicating that the refrigerators are not maintaining the desired temperature.

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Step-by-step explanation:

There are 720 ways to arrange the letters in the word GRIFFIN.

To see why, we can use the formula for permutations of a set with n elements, which is n! (n factorial).

The word GRIFFIN has 7 letters, so we have:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

However, since the letters in GRIFFIN are not all unique (there are 2 Fs and 2 Is), we need to divide by the number of ways the repeated letters can be arranged. This is the product of their factorials:

2! x 2! = 4

So the final answer is:

7! / (2! x 2!) = 5040 / 4 = 720

Examples of different arrangements of the letters in GRIFFIN are:

- FIGRINF

- IRGIFNF

- NGRIFFI

- IFRIGNF

- GFRINIF

- NRIGIFF

- FFIRIGN

And so on, for a total of 720 possible arrangements.

Does this answer your question.

Answer: 7,210,000

Step-by-step explanation:

Answer:

a)  112 cm

b)  4480 cm²

Step-by-step explanation:

Given:

The diameter of a circle is twice its radius. Therefore, the radius of the circle is:

[tex]\implies r=\dfrac{d}{2}=\dfrac{160}{2}=80\; \sf cm[/tex]

To find the length of the arc that subtends the given central angle θ on a circle of diameter d, use the arc length formula.

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Substitute the values into the formula:

[tex]\begin{aligned}\implies \sf Arc\; length&=r \theta\\&=80 \cdot 1.4\\&=112\; \sf cm\end{aligned}[/tex]

Therefore, the length of the arc that subtends the given central angle θ on a circle of diameter d is 112 cm.

To calculate the area of the sector determined by θ, we can use the area of a sector formula.

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

Substitute the values into the formula:

[tex]\begin{aligned}\implies \sf Area\;of\;a\;sector&=\dfrac{1}{2}r^2\theta\\\\&=\dfrac{1}{2} \cdot 80^2 \cdot 1.4\\\\&=\dfrac{1}{2} \cdot 6400 \cdot 1.4\\\\&=3200 \cdot 1.4\\\\&=4480\; \sf cm^2\end{aligned}[/tex]

Therefore, the area of the sector determined by θ is 4480 cm².

Therefore, the remainder when P(x) is divided by x - 5 is 3128.

The algebraic Remainder Theorem asserts that when a polynomial P(x) is divided by x-a, the division's remainder equals P(a). In other words, we can replace a for x in the polynomial and evaluate it if we have a polynomial P(x) and we want to know the remainder after it is divided by x-a. The remainder of the division will be the value.

Here,

So to find the remainder when P(x) is divided by x - 5, we need to evaluate P(5).

P(x) = 5x⁴ + 5x³ - 2x² - 5x + 3

P(5) = 5(5)⁴ + 5(5)³ - 2(5)² - 5(5) + 3

P(5) = 3128

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Negative correlation.

First of all, let's define the term "correlation" in math functions.

Correlation is a numeric value that expresses how strong the relation is between two variables. It also tells us how one functions affects the other. It can be calculated.

There are three classifications for correlations:

•  Positive correlation. This type of correlation indicates that when a variable increases in value, the other variable follows the same behavior.

•  Negative correlation. This correlation, on the other hand, indicates that when a variable increases, the other variables does the opposite, it decreases.

•  No correlation. This is when one variable has no effect over the other.

Check the attached image to see how these correlations look like in a graph.

On this question we are given a graph with several points on it. As you can tell, the more we move to the right on the "x" axis, the lower the points are. Therefore, as "x" increases, "y" decreases. This is a clear example of a negative correlation graph.

The value {( p ∧ q¹ )  → r¹ } is said to be a form of  expression that is  seen as a logical formula and it is then written in propositional logic made up of logical operators.

The logical operators are seen as  "and" (∧), "not" and  (→).

Note that the terms:

Therefore, the full formula {( p ∧ q¹ ) → r¹ } can then be said to be or read as "if (p and not q) is true, then not r is said to be true".

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See text below

{( p ∧ q¹ )  → r¹ }

For the estimated regression equation,

1. SST = 1946  SSR = 1602.747   SSE =  343.256

2. coefficient of determination r² = 0.824

3. The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. Option D

Looking at the estimated regression equation, Start by getting the Predicted Scores, which are;

21.257525 + 0.327425 x 180 = 80.194025

21.257525 + 0.327425 x 150 = 70.371275

21.257525 + 0.327425 x 95 = 52.3629

21.257525 + 0.327425 x 70 = 44.177275

21.257525 + 0.327425 x 70 = 44.177275

21.257525 + 0.327425 x 35 = 32.7174

Step 2, find mean

Mean = (74 + 73 + 59 + 56 + 38 + 24) / 6 = 54

SST = Σ(yi - y_mean)²

SST = (74 - 54)² + (73 - 54)² + (59 - 54)² + (56 - 54)² + (38 - 54)² + (24 - 54)² =1946

SSR = Σ(yi_predicted - y_mean)²

SSR = (80.194025 - 54)² + (70.371275 - 54)² + (52.3629 - 54)² + (44.177275 - 54)² + (44.177275 - 54)² + (32.7174 - 54)² = 1602.74660285

SSE = Σ(yi - yi_predicted)²

(74 - 80.194025)² + (73 - 70.371275)² + (59 - 52.3629)² + (56 - 44.177275)² + (38 - 44.177275)² + (24 - 32.7174)² = 343.255852847

r² = SSR / SST =  1602.747/1946 = 0.82361099691

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Answer:

The sum of angles in a quadrilateral is 360°.

  75° +125° +∠T +60° = 360°

  ∠T = 360° -260° = 100°

Step-by-step explanation:

C = 360 - 260 = 100 The answer is definitely 100 for T as well since the figures are similar. Answer 100 = T <<<<<<<

jcherry99 avatar

R = 75 and A therefore is 75. Now you have 3 angles whose value you know: D, A, and B. These three are 60 75 and 125. (125 is the second best answer). D + A + B = 60 + 75 + 125 = 260

jcherry99 avatar

If the figures are similar, then D = 60 and U = 60

jcherry99 avatar

D is on your left and U is on your left.

Answer:

PQRS is a rhombus with S2 =35° calculate the size of all interior angles

The total number of cups for sugar, juice and fruits are:

5cups of sugar

10 cups of juice

20 of fruits

To adjust the recipe for 30 servings, Joey needs to use proportional reasoning. If the original recipe serves 6, and Joey wants to make 30 servings, he needs to multiply the amount of each ingredient by 5.

Let's say the original recipe requires 1 cup of sugar, 2 cups of juice, and 4 cups of fruit. To find the total amount of each ingredient needed for 30 servings, we need to multiply each ingredient by 5:

1 cup of sugar x 5 = 5 cups of sugar

2 cups of juice x 5 = 10 cups of juice

4 cups of fruit x 5 = 20 cups of fruit

Therefore, Joey needs 5 cups of sugar, 10 cups of juice, and 20 cups of fruit to make fruit salad for 30 servings.

Let's  verify the calculations, we can use the ratio of the ingredients to the total number of servings:

1 cup of sugar : 2 cups of juice : 4 cups of fruit

For 6 servings, the ratio is:

1 cup of sugar x 1 : 2 cups of juice x 1 : 4 cups of fruit x 1 = 1:2:4

For 30 servings, the ratio becomes:

1 cup of sugar x 5 : 2 cups of juice x 5 : 4 cups of fruit x 5 = 5:10:20

Thus, we can see that the ratio is still the same, indicating that the adjusted recipe is correct.

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To find out the percentage of Tyrone's earnings that he saved, we need to divide the amount he saved by his total earnings and then multiply by 100 to convert the result into a percentage.

The amount that Tyrone saved is $24, and his total earnings are $60.

So,

Percentage of earnings saved = (Amount saved / Total earnings) x 100

= ($24 / $60) x 100

= 0.4 x 100

= 40%

Therefore, Tyrone saved 40% of his earnings by putting aside $24 from the $60 he earned mowing lawns.

Answer:

40%

Step-by-step explanation:

We Know

Tyrone saved $24 of the $60 he earned mowing lawns.

What percent of his earnings did he save?

We Take

(24 ÷ 60) x 100 = 40%

So, he saved 40% of his earning.

The sigma notation of the sum for this problem has the parameters given as follows:

To write the sigma notation for the sum in this problem, we must identify the pattern in the sum.

We have that in each term, a numerator of 1 is divided by the index n multiplied by one plus the index, hence the parameter B is given as follows:

B = 1/[n(n + 1)]

The last terms are 117 and 118, meaning that n = 117, hence the parameter A, representing the upper end of the sum, is given as follows:

A = 117.

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Answer:

(4/x) - 1 is the way to represent this equation.

Answer:

[tex]14000( {1.07}^{7} ) = 22480.94[/tex]

$22,480.94 > $20,400, so accepting the $14,000 prize now would be more profitable in 7 years.

The correct option is the third one, it can be written as the equation:

y = A*(1 - 0.073)ˣ

A general exponential decay can be written as:

y = A*(b)ˣ

Where A is the initial value, and b is the base.

It is an exponential decay only if 0 < b < 1.

From the given options, the one that can be modeled with an exponential decay is a car whose price depreciuates at a rate of 7.3% per year, because if the initial price of the car is A, we can write it as:

y = A*(1 - 0.073)ˣ

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Answer:

Give that the volume of the cylinder is 90cm³, the volume of the cone is (1/3)*90cm³ =30cm³

Answer:

your insurance will pay $165,000 for the damages to your home. You will have to pay the remaining $5,000 as your deductible.

Step-by-step explanation:

The amount that the person get after he home suffers $170,000 in damages is $-130000.

Deductible amount is the amount which is paid by one in the starting of any policy.

The homeowner’s policy has a premium of $150. Thus, the amount paid in a year is,

[tex]150\times12=1800[/tex]

The home suffers $170,000 in damages and the deductible is of $5000. Thus, the amount remain is,

[tex]\text{A}=170000-5000[/tex]

[tex]\text{A}=165000[/tex]

The limit of the policy is $300000. Thus, the amount will be remained as,

[tex]\text{A}=165000-300000[/tex]

[tex]\text{A}=-135000[/tex]

If we include the deductible amount, then,

[tex]\text{A}=-135000+5000[/tex]

[tex]\text{A}=-130000[/tex]

This amount does not include the premium paid by the homeowner. Hence the amount that the person get after he home suffers $170,000 in damages is $-130000.

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The missing step is −5x > −28. This is obtained by adding 14 to both sides of the inequality. Then, to get x < −2, we divide both sides by −5 and reverse the direction of the inequality sign.

The coordinate pairs that can be the end location are:

(-2, 10)

(-10, 10)

(-6, 14)

(-6, 4)

The student starts at (-6, 10) and walks 4 miles in some direction. Then the end location is any point of the form:

(-6 ± 4, 10)

or

(-6,10 ±4)

Then the 4 possible options are:

(-2, 10)

(-10, 10)

(-6, 14)

(-6, 4)

So these 4 are the correct options.

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The figure in which ∠1 is congruent to <2 is figure 2.

In Mathematics and Geometry, the vertical angles theorem is sometimes referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

By applying the vertical angles theorem to geometric figure 2, we have the following congruent angles:

m∠1 = m∠2 (same side interior and exterior angles are congruent).

In this context, we can reasonably infer and logically deduce that angle 1 is congruent to angle 2 in geometric figure 2 only.

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The relations between facing and bisected angle in the kite are proven as follows

3. The completed two column tables used to prove the specified relations are presented as follows;

Statement [tex]{}[/tex]                              Reasons

1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{AD}[/tex]      [tex]{}[/tex]                      1. Given

2. [tex]\overline{CB}[/tex]≅ [tex]\overline{CD}[/tex]    [tex]{}[/tex]                       2. Given

3. Construct [tex]\overline{AC}[/tex]                    3. Euclid's postulate #1

4. [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]                           4. Reflexive property

5. ΔABC ≅ ΔADC   [tex]{}[/tex]              5. SSS congruence rule

6. ∠ABC ≅ ∠ADC      [tex]{}[/tex]           6. CPCTC

4. The prove that the diagonals congruent sides bisect the angles.

Statement [tex]{}[/tex]                                Reasons

1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{AD}[/tex]                             1. Given

2. [tex]\overline{CB}[/tex] ≅ [tex]\overline{CD}[/tex]                           2. Given

3. Construct [tex]\overline{AC}[/tex]                     3. Euclid's postulate #1

4. [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]                            4. Reflexive property of congruence

5. ΔABC ≅ ΔADC    [tex]{}[/tex]              5. SSS congruence rule

6. ∠CAB ≅ ∠CAD [tex]{}[/tex]                 6. CPCTC

An angle bisector is a segment that divides an angle to form two angles of the same measure.

The details of the reasons used to prove the specified relations are presented as follows;

Euclid's postulate #1

Euclid's postulate #1 states that a straight line can be drawn from any one point to another point.

Reflexive property

The reflexive property of congruence states that a segment is congruent to itself

SSS congruence rule

The SSS, which is an acronym for Side-Side-Side, congruence rule states that the if three sides on one triangle are congruent to three sides on another triangle, then the two triangles are congruent

CPCTC

The acronym CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent.

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(a) The Null Hypothesis (H₀): The proportion of mall shoppers in my market category who would buy a subscription is greater than or equal to the proportion in Rachel's market category (P₂). Conversely, Alternatvie Hypothesis H₁ insinuates that this proportion is less.

(b) In order to evaluate the legitimacy of these speculations; we have decided to employ the z-test statistic.  

(c) In order to determine the test statistic: we will use the formula:

z = (p₁ - p₂) / √(p(1-p)(1/n₁ + 1/n₂))

where p = (x₁ + x₂) / (n₁ + n₂), where x₁ and x₂ denote the number of successes (or people who said they would purchase a subscription) in each sample, whereas n₁ and n₂ represent the sample sizes, respectively.

According to our data, we received the following: x₁ = 19, n₁ = 99, x₂ = 24, and n₂ = 107. Taking into consideration the aforementioned variables, we obtained p₁= 0.191, p₂= 0.224, and    P = 0.208 for the equation above. Therefore,  

z= (0.191 - 0.224)/√(0.208(1-0.208)(1/99+1/107)) ≈ -1.238

(rounded to three decimal places).

(d) For the single tailed test at 0.01 level of significance, the critical value generated by the z-test was -2.33.

(e) As a result of the calculated test statistic(-1.238) being greater than the produced critical value (-2.33); we cannot refute the null hypothesis. In other words, with an alpha of 0.01, we cannot conclude that the ratio of mall buyers in my market sector wanting to buy a subscription is less than that of the ones from Rachel's.

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The time(s) that the projectile to reach a height of 80 ft is 3.5 s and time to return to the ground is 1.5 seconds.

The equation of motion of the projectile is given as;

s = -16t² + v₀t

where;

when the height reached = 80 ft, the time of motion is calculated as;

-80 = -16t² + 32t

16t² - 32t - 80 = 0

t = 3.5 seconds or t = -1.5 seconds

Based on the negative sing, we can conclude that the time to return to the ground is 1.5 seconds.

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-3}x-4\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is -3 and it passes through (-2 , 5)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y -5 = - 3 ( x +2) \\\\\\ y-5=-3x-6\implies {\Large \begin{array}{llll} y=-3x-1 \end{array}}[/tex]