Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are complementary, then the sum of their measures is 90°.

Answer:

C

Step-by-step explanation:

Answer:

Jorge is using pencils at a rate of 6 packs a year or a rate of 2 packs every four months.

Step-by-step explanation:

1/3 of a year is four months so that would be 2 packs every four months and if you multiply that by three you’d get 12 month, or one year, and 6 packs of pencils.

Answer:

1

Step-by-step explanation:

because the 1 is actually invisible

its called invisible math

y=mx+b

Solving the set of equation by elimination method gives

x = 1.64

y = -0.727

The given data

4x - 2y = 8   (1)

5x + 3y = 6   (2)

multiplying (1) by 3/2 and adding the result to (2)

6x - 3y = 12

5x + 3y = 6

6x + 5x - 3y + 3y = 12 + 6

11x = 18

x = 18/11

x = 1.64

substitute x = 18/11 into (1)

4 * 18/11 - 2y = 8

72/11 - 2y = 8

2y = 72/11 - 8

2y = -16/11

y = -8/11

y = -0.727

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The equation of the lines passing the points and parallel to the equations ( 7,-3) , 3y = 12x + 5  (-5, -2), y + 3x = 10 is as follows:

The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form. Therefore, let's represent the line in slope intercept form.

The equation of a line in slope intercept form is as follows:

y = mx + b

where

Parallel line shave the same slope.

Hence,

( 7,-3) , 3y = 12x + 5

y = 4x + 5 / 3

slope is 4

The equation of the line is y = 4x + b. let's find the y-intercept using (7, -3).

-3 = 4(7) + b

b = -3 - 28

b = - 31

Hence, y = 4x  - 31

(-5, -2), y + 3x = 10

y = -3x + 10

slope = -3

Therefore, let's find y-intercept using (-5, -2)

-2 = -3(-5) + b

-2  = 15 + b

b = -2 -15

b = - 17

Therefore, y = -3x - 17.

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Answer:

2

Step-by-step explanation:

1/4 + 1/2 ÷ 3/8

0.25 + 0.5 ÷ 3/8

0.25 + 1.33

= 1.58

approximately 2

Answer:

Foot: 18.416666666666668

Yard: 6.1388888888888892836

The change in temperature is 15°

How to find Change in temperature ?

        t₂ = t₁ + final temperature

We have given,

In morning, when Rae woke up the temperature is (t₁) = -20°

At dinner time, the temperature is = 35°

t₂ = t₁ + 35

t₂ = (-20) + 35

t₂ = 15°

Hence, the change in temperature is 15°

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the decision rule for rejecting the null hypothesis is, to reject H₀ if t > 1.363.

Right-tailed test: H0µ = k H1:>k P-value = P(z>z x) This indicates the probability of obtaining a test statistic as high as or higher than z x. If the P-value is less than α, we reject H0(null hypothesis) and conclude that the data are statistically significant at the level α. We do not reject H0 if the P-value is greater than α.

H0: µ  = 5.3 , H1: µ> 5.3

it is a right-tailed test

n = 12

α = 0.10

therefore the decision rule for rejecting the null hypothesis is, Reject H0 if t> 1.363.

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Answer:

1000-400=600km

good luck i hope it helped, its all about reading the graph!

Answer:

200 miles

Step-by-step explanation:

if its 40 miles per hour then multiply 5 with 40 and you'll end up with 200 miles

Answer: $1.92

Step-by-step explanation:

This is the correct answer. Have a good day

Answer:

k=f(x)-ab^x-h

h=x-ln(f(x)/a-k/a)/ln(b)

a=f(x)/b^x-h - k/b^x-h

Answer: The correct answer is the one that has 4 + 5 + 2 + 3.

(I didn't say which side it is in case you got confused but it's the one right above the speaker sign.)

Step-by-step explanation:

A box plot is used to study the distribution and level of a set of a set of numbers. A box plot is made up of two lines and a box. The two lines are known as whiskers.

The end of the first whisker represents the minimum number. The minimum number is the smallest number in the dataset.  The end of the second whisker represents the maximum number. The maximum number is the largest number in the dataset.

The first line to the left represents the lower (first) quartile. The second line on the box represents the median. The third line on the box represents the upper (third) quartile.

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The value of sinθ = - 28/53, cosθ = - 45/53, tanθ = 28/45, cosecθ = -53/28, secθ = -53/45, cotθ = 45/28.

Given that:

The point (-90, -56) is on the terminal side of an angle, θ

Using Pythagoras' theorem,

Hypotenuse^2 = Perpendicular^2 + Base^2

Hypotenuse^2 = (-56)^2 + (-90)^2

Hypotenuse^2 = 3136 + 8100

Hypotenuse^2 = 11236

Hypotenuse = 106

The value of hypotenuse = 106

The exact value of the following is:

sinθ = Perpendicular/Hypotenuse = -56/106 = - 28/53

cosθ = Base/Hypotenuse = -90/106 = - 45/53

tanθ = Perpendicular/ Base = - 56/-90 = 28/45

cosecθ = 1/sinθ = -53/28

secθ = 1/cosθ = -53/45

cotθ = 1/tanθ = 45/28

Hence, we got all the values of θ.

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The probability that the sample standard deviations exceeds 3.5 hours more than 0.95 is 0.23 < 0.95 ..

The numbers of hours spent on watching television by a student in a weak before is normally distributed.

We have provide the following details, standard

deviations of sample ( Number of hours in weak) (σ) = 4.5 hours

sample size (n) = 30

we shall compute the mean and variance of sample .

The E of s squared is equal to 4.5 squared. The variance of S squared is equal to twice the square of sigma divided by 1, which is 30 minus 1, which is 28.6, 28.2817. The chi-square distribution here has 29 degrees of freedom, which equals 29 squared to 4.5 squared. We want to find probabilities greater than 90 because the standard deviation of our sample is greater than 3.5 hours. The probability that S squared is greater than 3.5 is The probability that chi-square with 29 degrees of freedom is greater than

17. 54321 is very high. This is the same as zero.

This is equal to 1 minus the probability that 29 degrees of freedom chi-square is greater than 51 points 5556, which is what we want for part B. we are given one Probability will be zero.

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#Complete question

The number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. A random sample of 30 students was taken.a. Is the probability more than 0.95 that the sample standard deviation exceeds 3.5 hours?b. Is the probability more than 0.95 that the sample standard deviation is less than 6 hours?

Answer:

can i have more info?

Step-by-step explanation:

The qualified student loan interest deduction in 2021 is $37500.

Adjusted gross income is an individual's total gross income less specific deductions in the United States income tax system. It is used to compute taxable income, which is AGI minus personal exemption and itemized deduction allowances. AGI is more important than gross income for most individual tax purposes.

AGI is calculated by taking your gross income and subtracting certain "above the line" deductions. 401(k) contributions, health savings account contributions, and educator expenses are common examples of deductions

As per Law, a maximum of $2,500 will be allowed to be deducted from the Income. Thus the following would be the solution.

Income of Sally Morris = $40,000

Less: Qualified student loan interest $2,500

Modified Adjusted Gross Income $37,500

The deduction is $37500.

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The turning point of the parabola is the point (2, - 9).

Quadratic equations represents parabolae and the vertex of the parabola represents the turning point as the slope of the curve changes its sign, from positive to negative or viceversa. The vertex can be derived by the vertex form of the equation of the parabola:

y - k = C · (x - h)²

Where:

Since the quadratic equation has two real coefficients, we need the location of two points on Cartesian plane to find one solution. First, create the system of linear equations:

b = - 5                                      (1)

5 · a + b = - 25                        (2)

Second, substitute b in (2) and clear a:

5 · a - 5 = - 25

5 · a = - 20

a = - 4

Third, write the quadratic equation:

y = x² - 4 · x - 5

Fourth, transform the equation into vertex form by completing the square:

y + 9 = x² - 4 · x + 4

y + 9 = (x - 2)²

Fifth, write the vertex of the parabola:

(h, k) = (2, - 9)

The point (2, - 9) represents the turning point of the parabola.

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Number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups

The ratio of cups of almonds to cups of peanuts in a mixed snack = 4 : 3

Number of of cups of almonds = 4x

Number of cups of peanuts = 3x

Total number of cups of mixed nuts snack = 49 cups

Then the equation will be

4x + 3x = 49

Add the like terms

7x = 49

x = 49 / 7

x = 7

Number of cups of almonds needed = 4x

= 4×7

= 28 cups

Number of cups of peanuts needed = 3x

= 3×7

= 21 cups

Hence, number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups

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The zero of the function lie between 2.5 and 3.0 and between 4.0 and 4.5

The given question is incomplete the complete question is

x      2.0    2.8    2.5    1.1    3.0   –0.8

f(x)    3.5   –1.2    4.0  –0.3  4.5     0.7

For the given table of values for a polynomial function, where must the zeros of the function lie?

A. between 2.0 and 2.5 and between 4.0 and 4.5

B. between 2.5 and 3.0 and between 4.0 and 4.5

C. between 2.0 and 2.5 and between 3.5 and 4.0

D. between 2.5 and 3.0 and between 3.5 and 4.0

answer : If a function is continuous and you have points on opposite sides of the x-axis, there must be a zero-crossing between those points. As evidenced by the table and graph,...

(3.0, 4.0) and (3.5, -0.2) 

are points on the x-axis on opposite sides. As a result, between x=3.0 and x=3.5, there must be a zero crossing.

In the same way,...

 (4.0, -0.8) and (4.5, 0.1) 

are points on the x-axis on opposite sides. As a result, between x=4.0 and x=4.5, there must be a zero-crossing.

The correct answer option includes both of these possible zero crossings.

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The linear equation to represent the hours that Yuson has left to do after x days is 16 - 2x.

From the information, Yuson has to do Y hours of community service.

She works two hours every day, so service hours in x days = 2x

Remaining service hours after x days = y-2x

Also we have after 8 days , Yuson has completed half of her required community serivice. Therefore,

8 = y/2.

Cross multiply

y = 16

So the linear equation is 16-2x.

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The best estimate of this amount of water is [tex]3*10^{7}[/tex].

Given:

At an elevation of 1221. 4 feet, lake mead will hold 28,945,000 acre-feet of water.

So, the amount of water that is in the lake will be 28,945,000 acre-feet which is estimated to be 30000000 acre-feet of water.

Because the nearest estimate to 28945000 is 30000000.

= 30000000

= 300000*[tex]10^{2}[/tex]

= 30000*[tex]10^{3}[/tex]

= 3000*[tex]10^{4}[/tex]

= 3*[tex]10^{3} *10^{4}[/tex]

= 3*[tex]10^{7}[/tex]

Therefore The best estimate of this amount of water is [tex]3*10^{7}[/tex].

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Kinematic parameters is the way by which coefficient of restitution change with angle of impact.

The ratio of a boulder's velocities or energy prior to and following its impact with the slope is represented by the coefficient of restitution, which is a dimensionless number. Different definitions of the coefficient of restitution have been put forth in earlier studies, but it has not been determined which definition is better suitable for predicting rockfall.

The determination of suitable values for the coefficients of restitution, which often change with the kinematic parameters and terrain conditions, is essential for the accuracy of a computer program modelling a rockfall trajectory. Using small-scale laboratory testing, the effects of the impact angle with regard to the slope on the coefficients of restitution have been identified and analyzed. to determine the validity of the current conclusion based on limited laboratory testing.

This study conducted a medium-scale laboratory test employing spherical limestone polyhedrons impacting concrete slabs to determine how the impact angle affects the coefficients of restitution when the test scale is changed. A 3D motion capture system measures the velocities before and after the collision during free fall tests. Several general laws apply when taking into account the impact angle's effect, regardless of the test scales and conditions, according to the results comparison between our test and the existing small-scale tests. The normal coefficient of restitution (Rn), the kinematic coefficient of restitution Rv, and the kinetic energy coefficient of restitution Re will all decrease as the impact angle increases.

In contrast, it will cause Rt's tangential coefficient of restitution to increase. The impact of the impact angle is significantly influenced by the rotation. The normal coefficient of restitution Rn and tangential coefficient of restitution Rt are always higher when more kinetic energy is converted to rotational energy.

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