Olivia rides her scooter 3/4 mile in 1/3 hour. What constant of proportionality relates the distance she travels to the time

i. α = 56°

ii. adj =  4.1

iii. opp = 2.79

We have to recall that what makes the right angle triangle unique is the fact that one of the angles that we find in the triangle is 90 degrees. We have to recall that the sum of the angles that we have in a triangle is 180°.

Hence we have;

α = 180 - (90 + 34)

α = 56°

Then;

Cos 34 = adj/5

adj = 5 cos 34

= 4.1

Sin 34 = opp/5

opp = 5 * sin 34

= 2.79

These are the parts of the right angled triangle required.

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The values of u and v in the table are directly proportional to each other with a constant k is 3.

When x increases, y increases; when x decreases, y decreases.

The opposite of direct is indirect. When x rises, y falls; when x falls, y rises.

If you said y is directly proportional to x,

it would be y/x=k or y=kx.

Here given that,

u = 0.25, 0.3, 0.1

v = 0.75, 0.9, 0.3

So here v = 3u

That is v = 3 x 0.25

v = 0.75

Hence u and v are directly proportional with a constant k = 3

When v = 2/5

To find u,

v = 3u

2/5 = 3u

u = 2/15

When u = 3/7

Then v = 3 x 3/7

v = 9/7

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Answer: -1/2

Step-by-step explanation:

The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.

Linearity is a property of equations with highest degree of 1. There isn't a single variable in it with an exponent greater than 1. The name "linear equation" comes from the fact that a linear equation always results in a straight line on a graph.

Linear equations in one variable and two variables are common in mathematics.

Two of lines' points on the plane are (1, 0)and (0, 9)

Lets put the value in the slope formula

y₂ - y₁ = m(x₂ - x₁)

9 - 0 = m(0 - 1)

9 = -m

m = -9

As we have the slope of the line lets put one of the values to get slope intercept form

y - y₁ = m(x - x₁)

y - 9 = -9(x - 0)

y = -9x + 9

Thus, The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.

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By taking the quotient between the total amount that she makes and the time of work, we will see that the rate of payment is $45 per hour.

The rate of payment is equal to the quotient between the amount she is paid and the time in which she works.

We know that Theresa wins $0.03 per word, and she can write 3000 words in 2 hours.

Then the amount that she wins is:

$0.03*3000 = $90

Then the rate of payment is:

$90/2 hours = $45 per hour.

Theresa wins 45 dollars per hour.

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There is enough evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.

At the null hypothesis, it is tested if the means are the same, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypothesis, it is tested if the means are different, hence:

[tex]H_0: \mu_1 - \mu_2 \neq 0[/tex]

For each sample, the mean and the standard error are given as follows:

Hence the mean and the standard error for the distribution of differences are given as follows:

The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:

z = -7/3.5119

z = -1.99.

We have a two-tailed test, as we are testing if the mean is different of a value.

Using a z-distribution calculator, with z = -1.99, and a two-tailed test, the p-value is given as follows:

0.0466.

As the p-value is less than the standard significance level of 0.05, there is enough evidence to conclude that Mrs. Smith and Mrs. Jones are not equally effective teachers.

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Answer: 23,760 feet

Step-by-step explanation:

1 mile = 5280 feet

4.5 * 5280 = 23,760

The number of sides that the polygon has is given as follows:

24 sides.

A regular polygon is a polygon in which all side lengths have the same measure, hence all the internal angles of the polygon will also have the same measure.

The sum of the internal angle measures of a polygon of n sides is given as follows:

S(n) = (n - 2) x 180º.

For a regular polygon of n sides, with n angles of equal measure, the measure of each interior angle is given as follows:

I = (n - 2) x 180/n.

In the case of the center of the polygon, the sum of the internal angles is of 360º, hence the number of sides n can be obtained as follows:

n  = 360/I.

For this problem, the internal angle measure is given as follows:

I = 15º.

Hence the number of sides is calculated as follows:

n = 360/15

n = 24 sides.

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The correct statement based on the number line is,

⇒ √68 is to the right of Point Q because it is greater than 8.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

The number line showing numbers from -8 to 8 in increments of 2, has point P at 0, and point Q is at 8.

Now, We know that;

⇒ √68 = 8.24

And,

⇒ 8.24 > 8

Hence, √68 is to the right of Point Q because it is greater than 8.

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Using the concept of ratio and proportions, the number of employees in A and B restaurant are 0.72 and 0.28

The relationship between two amounts of the same kind or that are linked is known as a proportion. It is used to compare the magnitude of one quantity to another and is typically expressed as a ratio or fraction. A percentage in mathematics is an equation proving the equality of two ratios.

In this problem, we have a total of 25 employees.

18 out of the 25 employees what to go to restaurant A.

The proportion of this is calculated as

18 / 25 = 0.72

Also, we have 7 employees that want to go to restaurant B

This is calculated as;

7 / 25 = 0.28

The proportion of employees that want to go to restaurant A and B are 0.72 and 0.28 respectively

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Complete Question:

A group of 25 employees want to go out for a group dinner.

18 employees want to go to Restaurant A.

7 employees want to go to Restaurant B.

Use this information to answer the questions below.

What is the proportion of employees who want to Restaurant A and B

Answer: 0.06 + 0.004

The probability for possibilities of x between P(X>4) and P(6.72<X<10.16)  is 0.5987 and 0.2351

X is N(5, 16)

means that, Z=(x-mean)/√variance = (x-5)/√4

=(x-5)/2

that is, Z is standard normal.

Then, by symmetry of the standard normal curve,

P(X>4)=P(X−5>4−5)

=P(X−54>4−54)

= P(Z>−14)

=P(Z>−.25)

=P(Z<.25)

= 0.5987.

Similarly

P(6.72<X<10.16)

= P(6.72−5<X−5<10.16−5)

=P(6.72−54<10.16−54)

=P(0.43<Z<1.29)

=P(Z<1.29)−P(Z<.43)

=.9015−.6664

= 0.2351.

Therefore, The probability for possibilities of x between P(X>4) and P(6.72<X<10.16)  is 0.5987 and 0.2351

Complete question - X is a normal random variable with mean=5 and variance=4 What are the possibilities for P(X>4) and P(6.72<X<10.16)?

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the slope is -4

hope this helps!!

Answer:

the slope is -4

Step-by-step explanation:

Answer:

3. f(3) = 16

4. h(3) = 4

Step-by-step explanation:

3.

f(x) = x² + 7

f(3) = 3² + 7

f(3) = 16

4.

h(x) = 12/x

h(3) = 12/3

h(3) = 4

Answer:

3/20.

Step-by-step explanation:

First of all remember that all triangles are always equal to 180 degrees from that we can figure out that x is is 70 because 30+80+70=180. z would be 40 because it is parallel to 40 and therefore equal to it. y is 100 because 40+40+100=180. Recap:

x: 70

z: 40

y: 100

If the APR on your credit card is current 31.2%. your monthly periodic rate is: 2.6%.

Using this formula to determine the monthly periodic rate

Monthly periodic rate = APR / 12 months

Where:

APR = Annual percentage rate = 31.2% or 0.312

Let plug in the formula

Monthly periodic rate = 0.312/12

Monthly periodic rate = 0.026 or 2.6%

Therefore we can conclude that the monthly periodic rate is 2.6%.

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Answer: To find the X and Y components of the 15N weight of the birthday cake, we can use trigonometry. We know that the angle of inclination of the table is 23° above the horizontal.

We can use the tangent function to find the X component of the weight, which is the component that is parallel to the table.

X = 15N * tangent (23°)

We can use the sine function to find the Y component of the weight, which is the component that is perpendicular to the table.

Y = 15N * sine (23°)

By applying these formulas and plugging in the angle and weight we can find the respective X and Y components.

Step-by-step explanation:

The value of p and w in the triangle are 6 units and 13√3 units respectively

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

In the triangle, we have angles of 30° and 90°

Using trigonometric ratios:

sin 30° = (2p+1)/(6p-10)     [sin = opp/hyp]

1/2 = (2p+1)/(6p-10)

1/2(6p-10) = (2p+1)

3p -5 = 2p + 1

3p -2p = 1+5

p = 6 units

cos 30° = w/(6p-10)       [cos = adj/hyp]

(√3)/2 = w/(6p-10)

(√3)/2 = w/((6×6) -10)

(√3)/2 = w/(36 -10)

(√3)/2 = w/26

w = (√3)/2 × 26

w = 13√3 units

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Answer: it’s 25

Step-by-step explanation:

15 +10

Answer:

13.389 = 13.4

The value of the evaluated iterated integral is 0.1202.

As per the given data the iterated integral is [tex]I & =\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex].

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as[tex]$\int_a^b f(x) d x$[/tex] = F(b) - F(a)

Here,

[tex]$\int=$[/tex] Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, [tex]$\int a b f(x) d x$[/tex] is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]I & =\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex]

Integrate the given iterated integral.

We get:

[tex]& =\int_0^1 \cos \left(s^7\right)\left(\int_0^{s^6} d t\right) d s[/tex]

[tex]& =\int_0^1 \cos \left(s^7\right) \times[t]_0^{s^6} d s . \\[/tex]

[tex]& =\int_0^1 \cos \left(s^7\right) \times\left(s^6-0\right) d s . \\[/tex]

[tex]& =\int_0^1 s^6 \cos \left(s^7\right) d s[/tex]

Say [tex]s^7=t[/tex]                 when s = 0

[tex]\Rightarrow \frac{d t}{d s}=7 s^6 \quad$[/tex]                          t = 0  

[tex]\Rightarrow \frac{d t}{7}=s^6 d s[/tex]              when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

[tex]$I=\int_0^1 \cos (t) \frac{d t}{7}$[/tex]

[tex]$=\frac{1}{7} \int_0^1 \cos (t) d t$[/tex]

[tex]$=\frac{1}{7}[\sin (t)]_0^1=\frac{1}{7}[\sin (1)-\sin (0)]$[/tex]

[tex]=\frac{\sin (1)}{7}$[/tex]

[tex]\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex] = 0.1202

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The two factors of the first number 28 that their sum is will be equal to the second number 16 are 2 and 14.

Factor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.

The first number 28 have the following factors:

1, 2, 4, 7, 14, and 28.

the factors 2 and 14 are the factors we need because;

2 × 14 = 28

2 + 14 = 16

Therefore, 2 and 14 are the two factors of 28 that their product is the first number 28 and their sum is the second number 16.

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c.The graph of G(x) is the graph of F(x) stretched vertically flipped over the x axis and shifted 4 units to the left.

A diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair is known as graph.

Here,

Given :

Suppose that F(x) = x² and G(x)

compares the graph of G(x) with the graph of F(x)

-(x+4)².

Thus , the solution by observing the given information is:

So, it is

C.The graph of G(x) is the graph of F(x) stretched vertically flipped over the x axis and shifted 4 units to the left.

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The distance travelled by larger circular wheel is 2π(R-r) more than the distance travelled by old tires.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now

let radius of old tires =r

radius of new tires =R

distance travelled by new tire in one rotation= 2πR

distance travelled by old tire=2πr

Hence,

            The distance travelled by larger circular wheel is 2π(R-r)  more than the distance travelled by old tires.

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The solution's f[x] means f(x)=0 when x is not in [−2,2]

The answer to [-2,2] is: f(x)dx=P(X∈dx)=2∗(2−|x|)dx4∗(12∗2∗2)=14(2−|x|)dx

Consequently, f(x)=14(2|x|) on [2,2]

and if not, f(x)=0

For [2,0], it is 14(2+x), while for [2,0], it is 14(2-x).

I discovered a formula for the uniform distribution U=X for (a,b), however, I don't believe this is right since the answer would then be X+24 without X being an absolute value. It also doesn't apply to other questions of a similar nature.

Please assist; there is a very strange exercise question in the textbook that we are unable to solve on our own. I have no idea how they obtained the 2(2|x|)dx4(12|2]).

Furthermore,  f(x) may indicate f(x)=0 when x is not in [2,2].

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The Full question would be:

Consider a point picked uniformly at random from the area inside the shape with the coordinates (-2,0), (0,2), (2,0), (0,-2).

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