Find the slope of the question below

The equation will be t = 3s where t is total cost and s is number of snow cones. this can be find out be relationship of number of snow cones and total cost in table .

In given table :

Number of snow cones               Total cost

2                                                      6

6                                                      12

5                                                      15

From above table, we can relate

1st case :
number of snow cones = 2 and total cost = 6

i.e. 3 times of number of cones.

2nd case:

number of cones = 4 and total cost = 12

i.e. 3 times the number of cones.

3rd case :

number of cones = 5 and total cost = 15

i.e. 3 times the number of cones.

So, we see same pattern is repeated in all.

Then equation will be t = 3s where t = total cost , s = number of snow cones.

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The trade this country will import is given by the option (C) 300 pair of shoes.

The number of shoes exported will be calculated by the formula -

Import = quantity demanded - quantity supplied. The formula is based on the concept that the import of shoes will be carried out once the manufacturing is more than the demand.

The graph indicates the quantity demanded is 1000 and the quantity supplied is 1300. Keep the values in formula to find imports.

Imports = 1300 - 1000

Performing subtraction on Right Hand Side of the equation

Imports = 300

Hence, the import is 300.

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The complete question is attached in figure.

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

[tex]\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}[/tex]

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.  

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

[tex]\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}[/tex]

72 mph = 105.6 ft/second

In order to convert any value from mph the following formula can be referred to:

speed in miles per hour x  5,280 = speed in foot per second

Therefore when 72 miles per hour is converted to foot per second would equal to the following value:

105.6 feet per second

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This is one way of writing a quadratic function:

[tex]f(x)= a(x-h)^2+k[/tex]

We're given:

[tex]f(x) = -6x^2 - 60x - 151[/tex]

To write a quadratic function in vertex form, we must complete the square.

⇒ Put parentheses around the first two terms containing x and x²:

[tex]f(x) = (-6x^2 - 60x) - 151[/tex]

⇒ Factor out -6 (keeping the x's in the parentheses):

[tex]f(x) = -6(x^2+10x) - 151[/tex]

⇒ To complete the square, add, inside the parentheses, the square of half the coefficient of x.

[tex]f(x) = -6(x^2+10x+25) - 151[/tex]

⇒ Now, we cannot randomly introduce a new value into a function. To balance the +25, subtract -6(25) outside the parentheses:

[tex]f(x) = -6(x^2+10x+25) - 151-(-6*25)\\f(x) = -6(x^2+10x+25) - 151-(-150)\\f(x) = -6(x^2+10x+25) - 151+150\\f(x) = -6(x^2+10x+25) - 1[/tex]

⇒ Finally, complete the square.

[tex]f(x) = -6(x+5)^2 - 1[/tex]

[tex]f(x) = -6(x+5)^2 - 1[/tex]

Let V be a finite-dimensional vector space and let B ={α 1…,α n } be a basis for V . Let ( | ) be the inner product of V. If c 1,...,c n , are n is a scalar, then show that there exist one vector α∈ V such that (α∣αj)=cj, j=1 ,…,n.

We have given that V is a finite dimensional vector space.

Consider α∈ V defined as

α = α₁β₁ + α₂β₂ + -----+ αₙβₙ where,

β₁ = α₁

β₂= α₂ - (α₁ |β₁)/β₁/β₂ |(β₁)

similarly, __

βⱼ = αⱼ - ( ∑ (αⱼ|βⱼ) / βᵢ|(βᵢ) βᵢ ) , j = 2,n bar

As defined aᵢ, i = 1, j bar

α₁ = c₁/ (β₁ )|β₁

___

α₂ = c₁/ (β₁ )|β₁ - a₁ ( α₂|β₂/β₁|β₂)

proceeding like as we get

_______

αⱼ = 1/β₁|(β₁) (cⱼ - ∑ αⱼ ( αⱼ |βⱼ)

then conider

(α|αⱼ )= ( α₁β₁ + α₂β₂ + -- + αₙβₙ |αⱼ )

= α₁β₁ + α₂β₂ + -- + αₙβₙ |βⱼ ) + ∑ α₁β₁+ α₂β₂ +---+αⱼβᵢ /βᵢβᵢ)

______

(α|αⱼ) =αⱼ(βⱼ |βⱼ) + (cⱼ - ∑ αⱼ ( αⱼ |βⱼ) βⱼ |βⱼ

__ ___

= (cⱼ - ∑ αᵢ ( αⱼ |βᵢ) + ∑αⱼ |βᵢ

(α|αⱼ) = cj, j = 1,n

Hence proved.

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If the owner's beliefs are correct,  Event A and Event B are not mutually exclusive and are independent and must be true for event A and event B.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative. In the sections that follow, let's go into greater detail on the fundamentals of probability.

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The measure of the angle ∠BDC is 68°.

What is the straight line angle?

A straight angle in geometry is one that is 180 degrees in length. It looks like a straight line, which is why it is known as a straight angle. In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.

We have,

∠BDA is a straight angle

so ∠BDA = 180°

We need to find the ∠BDC

∠CDA = -8x + 48°

∠BDC = -7x + 12°

∠BDA = ∠BDC + ∠CDA = 180°

(-8x + 48°) + (-7x + 12°) = 180°

-15x + 60° = 180°

-15x = 120°

x = -8°

∠BDC = -7x + 12°

= -7(-8°) + 12°

= 56° + 12°

= 68°

Hence, the measure of the angle ∠BDC is 68°.

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Everything else is being equal, but we prefer an unbiased estimator mostly compare to a biased estimator because a biased estimator may be used for a variety of reasons, such as the difficulty of computing an unbiased estimator (as in the case of estimating standard deviation).

The fact that a biased estimator may be unbiased with respect to different measures, and the fact that an unbiased estimator does not exist without further assumptions about a population. Thus, it's miles scientifically now no longer accurate to apply a biased estimator for a parameter while there may be an independent estimator for it.

Only in unavoidable situation, it's miles cautioned to apply a biased estimator (which need to be consistent) for a parameter while there may be no independent estimator for it. It could be anticipated that a terrific estimator need to bring about an estimate this is near the real cost of the parameter. Because in exercise the parameters are unknown, it isn't always viable to evaluate the estimate with the real cost. Unbiasedness serves as a degree of closeness among an estimator and the parameter.

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The amount of the investment at a rate of 7% for 6 months will be $2200.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Harriett Weiss procured $77 in straightforward premium in a half year at a yearly loan fee of 7%.

Then the amount of the investment is given as,

$77 = [P x 7 x (6/12)]/100

$7700 = P x 7 x 1/2

7P = $15400

P = $2200

The amount of the investment at a rate of 7% for 6 months will be $2200.

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By solving a linear equation, it can be calculated that the value of 3x - 4 is 8

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

[tex]\frac{3}{4}x - 2 = 1\\\frac{3}{4}x = 1 + 2\\\frac{3}{4}x = 3\\x = \frac{3 \times 4}{3}\\x = 4\\[/tex]

Value of 3x - 4  = [tex]3 \times 4 - 4 \\[/tex]

                          = 12 - 4

                          = 8

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Answer:

  b.  40

Step-by-step explanation:

You want the missing leg length in a right triangle with one side of length 9 and the hypotenuse of length 41.

The missing side of any triangle will be between the sum and difference of the other two side lengths.

  c-a < b < c+a

  32 < b < 50

In a right triangle, every side length is less than the length of the hypotenuse:

  b < c

  32 < b < 41

There is only one answer choice in this range: b = 40.

__

Additional comment

You can make use of your knowledge of Pythagorean triples. One of them is {9, 40, 41}, which tells you that b=40.

Or, you can use the Pythagorean theorem to compute b:

  a² +b² = c²

  9² +b² = 41²

  b² = 1681 -81 = 1600

  b = √1600 = 40

For any odd integer, there is a Pythagorean triple with sides 1 unit apart such that those longer side lengths are about half of the square of that odd integer:

  9² = 81 = 40+41

so {9, 40, 41} is a Pythagorean triple.

The simplest of these is ...

  3² = 9 = 4+5   ⇒   {3, 4, 5} is a Pythagorean triple.

Answer:

Step-by-step explanation:

1. Inequality will switch

2. Inequality will stay the same

3. Inequality will stay the same

4. Inequality will switch

The given confidence interval is correct and it is between 22% to 38%.

The formula for calculating the confidence interval of population proportion is

[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]

Here the sample proportion is represented by [tex]\bar{p}[/tex].

It is given that,

The 95% confidence interval has a sample size of n = 120 and the number of successes = 36.

So, the sample proportion [tex]\bar{p}[/tex] = 36/120 = 0.3

For the 95% confidence interval, α = 1 - 0.95 = 0.05

And α/2 = 0.05/2 = 0.025

Then, the z-score for α/2 = 0.025 is [tex]z{\alpha/2|=1.96[/tex].

And the standard deviation, [tex]\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }=\sqrt{\frac{0.3(1-0.3)}{120} }[/tex] = 0.0418

So, the interval is in between

C.I = 0.3 ± 1.96 × 0.0418

Upper limit = 0.3 + 1.96 × 0.0418 = 0.38 = 38%

Lower limit = 0.3 - 1.96 × 0.0418 = 0.218 = 0.22 = 22%

Therefore, the given confidence interval is correct.

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The equation of the verticallly-oriented ellipse is x²/4 + y²/25 = 1

The equation of a vertically-oriented ellipse centered at the origin with major axis y axis is given by

x²/b² + y²/a² = 1 where a > b

Given that the vertically-oriented ellipse centered at (0,0) with a full major y-axis length of 10 units and a full minor x-axis length of 4 units.

We have that the length of major axis 2a = 10

⇒ a = 10/2

⇒ a = 5

Also, the length of minor axis 2b = 4

⇒ a = 4/2

⇒ a = 2

So, given the equation of the vertically-oriented ellipse,

x²/b² + y²/a² = 1 where a > b

Substituting the values of the variables into the equation, we have that

x²/b² + y²/a² = 1 where a > b

x²/2² + y²/5² = 1

x²/4 + y²/25 = 1

So, the equation is x²/4 + y²/25 = 1

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On solving the question - Use the z distribution if the population variances are known; if not, use the -tdf distribution.

A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.

The difference between the mean and the mean squared is known as the variance, and the standard deviation is the square root of that difference. Although in different units, both measurements capture the distribution's variability. The same units are used to express standard deviation and the original value.

Use the z distribution if the population variances are known; if not, use the -tdf distribution.

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The histogram that represents the data-set in this problem is given by the image shown at the end of the answer.

An histogram is a graph that shows the number of times each element of x was observed.

For this problem, the elements are divided in ranges, hence the histogram will give the number of elements in each range that was observed.

The ranges for this histogram are given as follows:

The number of elements in each range is given as follows:

Meaning that the third histogram, from the top down, is the correct option.

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Answer: 792 Combinations

Answer:

here this should help you

The angles in order from the smallest to the largest are ∠E < ∠D < ∠F.

Option D is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

∠D is opposite to the side length 15.

∠E is opposite to the side length 14.

∠E is the smallest angle.

∠F is opposite to the side length 23.

∠F is the largest angle.

Thus,

∠E < ∠D < ∠F

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the inequality of the number line will be -6<x<2.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

In this number line the max point its marked is 2

and the minimum point is -6

So the value of unknown x should lie in between

-6<x<2

So, the inequality of the number line will be -6<x<2.

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Answer:

6

Step-by-step explanation:

3 is 3/5 of 5 therefore 6 would be 3/5 of 10 and the triangles are similar so

Therefore the value of function f(g(x)) comes out to be x[tex]e^{2}[/tex] +[tex]e^{2}[/tex]-3

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. If anything is entered for x, there is just one output for y. Since x is the input value, we can state that y is a function of x.

Here,

Given: f(x)=x[tex]e^{2}[/tex]-3  and g(x)=x+1

To find the value of f(g(x))

we put g(x) in f(x)

So,

=> f(g(x))= g(x)[tex]e^{2}[/tex]-3

=>f(g(x))= (x+1)[tex]e^{2}[/tex]-3

=> f(g(x))= x[tex]e^{2}[/tex] +[tex]e^{2}[/tex]-3

Therefore the value of function f(g(x)) comes out to be x[tex]e^{2}[/tex] +[tex]e^{2}[/tex]-3

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Answer: 3 pieces

Step-by-step explanation:

This problem can be solved by modeling the problem using equivalent fractions.

We know Stephanie put icing on 9 of her 15 pieces, this gives us a fraction of [tex]\frac{9}{15}[/tex].

Tammy cut her cake in 5 pieces, but we do not know how many were iced, the pieces of iced cake will be our variable, x, so her fraction is [tex]\frac{x}{5}[/tex].

Both of the fractions need to be equivalent so [tex]\frac{9}{15} =\frac{x}{5}[/tex], which can be solved for x = 3 pieces.

Answer:

d = h(cot1 - cot2)

d = 100(cot30 - cot45))

d = 100* (1.732 - 1)

d = 100*0.732

d = 73.2 m

a) The approximate mean shipping time: X{bar} = 1.64

b) The approximate variance and standard deviation:

S² = 27.03, σ = 5.2

In this question, we have been given the frequency distribution of shipping times (number of hours between the time an order is placed and the time the order is shipped) for a random sample of 40 orders.

We need to find the approximate mean shipping time, variance and standard deviation.

Number of Hours        fi                midpoint

      4 < 10                  8                    7

     10 < 16                15                  13

     16 < 22                10                  19

     22 < 28                  7                   25

       SUM:                  40

a) the approximate mean shipping time:

X{bar} = (7.8 + 13.15 + 19.10 + 25.7)/40

X{bar} = 65.75/40

X{bar} = 1.64

b) the approximate variance:

S² = [(7.8 - 1.64)² + (13.15 - 1.64)²+(19.10 - 1.64)²+(25.7 - 1.64)²] / 39

S² = 1054.16/39

S² = 27.03

And the standard deviation:

σ = √S²

σ = √27.03

σ = 5.2

Therefore, for given frequency distribution,

a) mean = 1.64

b) variance = 27.03 and standard deviation = 5.2

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The chi-square test is 5.02 higher than critical value 3.841 so the two states does not differ with regards of shopping habits, and p value is 0.025.

O = observed value

E = expected value

n = size of sample = 2

df = degree of freedom = n - 1 = 2 - 1

α = significance level = 5% = 0.05

Chi-square is a one of many test statistic, chi-square is a test to see the different from observed value and expected value.

Chi-square formula is,

[tex]\chi^2[/tex] = [tex]\sum\frac{(O_i - E_i)^2}{E_i}[/tex]

Since, in question only give us the observed value, we need to calculate the expected value first.

Expected value conscientious state A can be calculate by this formula

E(ca) = total of state A value × total of conscientious value ÷ grand total

Repeat this process to all observed value.

We use excel to simplified and for precise calculation. Then, we put the obtained value from excel formula to Chi-square formula,

[tex]\chi^2[/tex] = 0.69 + 1.69 + 0.76 + 1.88

= 5.02

a) Critical value for df = 1 and α = 0.05 from chi-square table is 3.841

Since, the result is 5.02 higher than 3.841, it can be concluded that the two states does not differ with regards of shopping habits.

Assumptions for we use is the study group is independent and the each expected value is higher than 5.

b) We use chi-square p-value calculator with P([tex]\chi^2[/tex] > 5.02) and df = 1, α = 0.05. So, we get 0.025.

Thus, two states doesn't differ with regards of shopping habits since chi-square result is higher than critical value, and p value is 0.025.

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Answer: 9x

Step-by-step explanation:

-4x+y=5x

solve for x

y=9x