Ted ran three miles in 2.8 minutes. At this rate, how long would it take him to run 33.3 miles?​

Solution:

Draw the parallelogram on the coordinate plane.

We can tell that the intersection point is (-8/5,27/10).

Hoped this helped!

Answer:

x=3

Step-by-step explanation:

● -3 (-4x+4) = 15 + 3x

Multiply -3 by (-4x+4) first

● (-3) × (-4x) + (-3)×(4) = 15 + 3x

● 12 x - 12 = 15 +3x

Add 12 to both sides

● 12x - 12 + 12 = 15 + 3x +12

● 12 x = 27 + 3x

Substract 3x from both sides

● 12x -3x = 27 + 3x - 3x

● 9x = 27

Dividr both sides by 9

● 9x/9 = 27/9

● x = 3

Answer:

x = 6.24

Step-by-step explanation:

x =

Tan32° = OPP/ADJ

Tan32° = x/10

0.624 = x/10

cross-multiply

x = 6.24

1. An equation that represents "the amount of tax on an item of price p",

t = p x X / 100

2. Marta does pay on an item whose price is $20, $1.6

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Tax rate = 8%

1. Let's assume that the sales tax rate is X%.

Then, the equation that represents the amount of tax (t) Marta pays on an item whose price is p can be written as:

t = p x X / 100

2. If the price of the item is $20, the amount of tax Marta pays can be calculated as follows:

t = $20 x X / 100

t = $20 x 8 / 100

t = $1.6

So, Marta pays $1.6 in sales tax on an item whose price is $100.

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Answer:

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is 0.0537.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is 0.0023.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is 0.1101.

Step-by-step explanation:

We are given that according to an NRF survey conducted by BIG research, the average family spends about $237 on electronics in back-to-college spending per student.

Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54.

Let X = back-to-college family spending on electronics

SO, X ~ Normal(\(\mu=237,\sigma^{2} =54^{2}\))

The z score probability distribution for normal distribution is given by;

                                 Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = population mean family spending = $237

           \(\sigma\) = standard deviation = $54

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is = P(X < $150)

        P(X < $150) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{150-237}{54}\) ) = P(Z < -1.61) = 1 - P(Z \(\leq\) 1.61)

                                                             = 1 - 0.9463 = 0.0537

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9463.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is = P(X > $390)

        P(X > $390) = P( \(\frac{X-\mu}{\sigma}\) > \(\frac{390-237}{54}\) ) = P(Z > 2.83) = 1 - P(Z \(\leq\) 2.83)

                                                             = 1 - 0.9977 = 0.0023

The above probability is calculated by looking at the value of x = 2.83 in the z table which has an area of 0.9977.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is given by = P($120 < X < $175)

     P($120 < X < $175) = P(X < $175) - P(X \(\leq\) $120)

     P(X < $175) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{175-237}{54}\) ) = P(Z < -1.15) = 1 - P(Z \(\leq\) 1.15)

                                                         = 1 - 0.8749 = 0.1251

     P(X < $120) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{120-237}{54}\) ) = P(Z < -2.17) = 1 - P(Z \(\leq\) 2.17)

                                                         = 1 - 0.9850 = 0.015

The above probability is calculated by looking at the value of x = 1.15 and x = 2.17 in the z table which has an area of 0.8749 and 0.9850 respectively.

Therefore, P($120 < X < $175) = 0.1251 - 0.015 = 0.1101

Answer:

268

Step-by-step explanation:

4 times 67

Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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Answer:

\((u \circ w)(2) = -34\)

\((w \circ u) = -49\)

Step-by-step explanation:

We are given these following functions:

\(u(x) = 4x + 2\)

\(w(x) = -5x + 1\)

The first step to solve this question is finding the composite functions. So

\((u \circ w)(x) = u(w(x)) = u(-5x+1) = 4(-5x + 1) + 2 = -20x + 6\)

\((w \circ u)(x) = w(u(x)) = w(4x + 2) = -5(4x+2) + 1 = -20x - 9\)

At x = 2

Now we replace x by 2 in each of the functions. So

\((u \circ w)(2) = -20(2) + 6 = -40 + 6 = -34\)

\((w \circ u)(2) = -20(2) - 9 = -40 - 9 = -49\)

False, In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.

What is exponential decay function?

In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time.

                     It can be written as y=a(1-b)x, where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.

How do you calculate an exponential function?

The equation f(x) = ax, in which the input variable x appears as an exponent, describes an exponential function. Both the exponential function and the value of x are dependent on the exponential curve.

                               The exponential function, which has the form, is a significant mathematical function. f(x) = ax.

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A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.

We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding

m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.

m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.

m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).

m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.

m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

Based on the above analysis, the statements that are always true regarding the diagram are

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°

m∠2 + m∠3 + m∠5 = 180°

Therefore, the correct options are B, C, and E.

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Two triangles cannot be proven to be congruent using the method: A. Prove all sets of corresponding angles are congruent.

Two triangles are congruent to each other if they have the same shape and the same size, that is, all three sets of corresponding sides and all three sets of corresponding angles of the two triangles are congruent to each other.

Also, the following condition or criteria can be used to determine if two triangles are congruent to each other:

Thus, the method that cannot be used is: A. Prove all sets of corresponding angles are congruent.

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Answer:

John earns $14.00 for two hours of work.

Step-by-step explanation:

Answer:

56 degrees

Step-by-step explanation:

Here, I think you just accidentally put the value for the angle ZWX, which would be ZWP+PWX(56+56).

You actually already wrote it on the paper, so nothing wrong with your math here, just a thinking error :)

The distance between the points M=(-4, 9 ) and L=(-1. 1) in the coordinate plane is \(\sqrt{73}\).

Explain Coordinate Plane.

In a plane, a Cartesian coordinate system is a system of a coordinate that designates each point uniquely by a pair of numerical coordinate in a plane, which are the signed distances from two fixed perpendicular oriented lines to the point on the same plane, measured in the same unit of length.

Solution Explained:

Using the distance formula, we have

\(\sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2} }\)

Substituting the values using the values of the points

\(\sqrt{(-1 + 4) ^{2} + (1 - 9) ^{2} }\)

\(\sqrt{(3) ^{2} + (-8) ^{2} }\)

\(\sqrt{9 + 64}\)

\(\sqrt{73}\)

Hence, the distance between the two points is \(\sqrt{73}\)

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Answer: 5 weeks

Step-by-step explanation: You took 8 quizzes over 2 weeks. Start at 2 weeks which is 8. Divide 8 by 2 to get 4. each half a week is 4 quizzes. subtract 8 from 20 which is 12. Divide 12 by 4 which you get 3. Add the 2 weeks to the 3 to get 5 weeks.

Answer:

Step-by-step explanation:

Answer: 6(x+7)° = 24(x-8)°

Step-by-step explanation:
We know that both angles are equal as they are alternate exterior angles.

6(x+7)=24(x-8)

6x+42=24x-192

6x -6x +42 +192 =24x -6x -192 +192

234 = 18x

18x/18 = 234/18

x = 13

And then for question B and C, you need to calculate the expression with x being equal to 13.

Answer:

Below

Step-by-step explanation:

csc^2  = 1/sin^2

sin ( x/2) = +- sqrt (( 1-cos x)/2)    <====half angle identity

so csc^2 (x/2) becomes :    1/ ((1-cos x)/2) = 2/ ( 1-cos x)

Answer: I rate the wind 5 stars.

Step-by-step explanation:

Gives us some fresh air when we go outside.

Answer:

E( -2, -1.5)

Explanation:

First, we need to identify the coordinates of C and D, so the coordinates are:

C(1, 6)

D(-3, -4)

Now, if E divides CD three-fourths of the way from C to D, we can use the following equation to find the coordinates of E:

Where Ex is the coordinate of E in x, Ey is the coordinate of E in y, (x1, y1) are the coordinates of C, and (x2, y2) are the coordinates of D. So, replacing (x1, y1) by (1, 6) and (x2, y2) by (-3, -4), we get:

So, the coordinates of point E is (-2, -1.5) and the graph is:

The side x of the triangular base prism is 0.4 centimetres.

The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,

c²= a² + b²

where

Therefore,

x² = 0.5² - 0.3²

x² = 0.25 - 0.09

x = √0.16

x = 0.4 cm

Therefore,

x = 0.4 centimetres.

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Answer:

1. 3 × Equation [A2] --> Equation [B2]

2. 4 × Equation [B1] + Equation [B2] --> Equation [C2]

Step-by-step explanation:

1. 3 × Equation [A2] --> Equation [B2]

Technically 1 x equation [A1] --> equation [B2] works, but I doubt you're meant to do that lol

Instead, this works:

4x × 3 = 12x

-7y × 3 = -21y

8 × 3 = 24

2. 4 × Equation [B1] + Equation [B2] --> Equation [C2]

(-3x × 4) + 12x = -12x + 12x = 0x

(2y × 4) + -21y = 8y - 21y = -13y

(7 × 4) + 28 = 28 + 24 = 52

=========================

I'll try to explain my process a little this time.

From A to B, you can see that equation 2 changed. Looking at the first term, 4x changed to 12x. Thats a multiplier of 3, and you can check that on the rest. In this case, that works.

Then from B to C, equation 2 changed again. This time, I noticed that x was canceled out. That means -12x had to have been added to 12x. In equation 1, theres a -3x. 4 times that is -12, and adding -12x to equation 2 works. Check that with the rest, and they all work.

Answer:

32 tablespoons are in 1 pint

Step-by-step explanation:

1/4 cup = 4 tablespoons

2/4 = 8 tablespoons

3/4 = 12 tablespoons

4/4 (1 cup) = 16 tablespoons

16*2 = 32

1 pint = 2 cups = 32 tablespoons

Digoxin has a half-life of 35 hours, so it takes 70 hours for the toxic plasma concentration to decline to a therapeutic plasma concentration of 2ng/ML.

Digoxin has a half-life of 35 hours, which means it takes 35 hours for the quantity of digoxin in the body to be decreased by half. The dangerous plasma concentration of 8ng/ML must be decreased to a therapeutic plasma concentration of 2ng/ML in this circumstance.

To calculate how long this will take, we need to use the formula:

Time = (Toxic Concentration - Therapeutic Concentration) / (0.5 x Half-Life)

Time = (8ng/ML - 2ng/ML) / (0.5 x 35hrs)

Time = 6ng/ML / (17.5hrs)

Time = 0.342hrs

Time = 70hrs

As a result, the dangerous plasma concentration of 8ng/ML will take 70 hours to decrease to a therapeutic plasma concentration of 2ng/ML.

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The answer is A

Hope this helps!

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

A rare card, as the law of supply and demand states that if demand (the rarity) exceeds supply, prices will rise.

Step-by-step explanation:

Answer:

28.1

Step-by-step explanation:

140.50/5

These are some expensive pens

Answer:

$28.1

Step-by-step explanation:

Divide

140.50 divided by 5 = 28.1

(That's an expensive pen)

Answer: 242

Step-by-step explanation:

Answer:

It is 363

Step-by-step explanation: