Anna is saving up for a new cell phone that costs $300. She has $150 already saved
She makes $10 an hour babysitting. How many hours does she need to babysit to buy
the new cell phone?

The vectors u and v are orthogonal, and their magnitudes are equal to 1. Hence, the set {u, v} is an orthonormal set.

To determine if the set of vectors {u, v} is orthonormal, we need to check if the vectors are orthogonal and if their magnitudes are equal to 1.

First, let's check if the vectors u and v are orthogonal. Two vectors are orthogonal if their dot product is zero.

The dot product of u and v is given by:

u · v = (-0.6)(-0.8) + (-0.8)(0.6) = 0.48 - 0.48 = 0

Since the dot product of u and v is zero, we can conclude that the vectors u and v are orthogonal.

Next, let's check if the magnitude of vector u is equal to 1. The magnitude of a vector u = (u1, u2) is given by:

|u| = √(u1² + u2²)

Substituting the values of u = (-0.6, -0.8):

|u| = √((-0.6)² + (-0.8)²) = √(0.36 + 0.64) = √1 = 1

The magnitude of vector u is equal to 1.

Similarly, let's check the magnitude of vector v. The magnitude of vector v = (-0.8, 0.6) is given by:

|v| = √((-0.8)² + (0.6)²) = √(0.64 + 0.36) = √1 = 1

The magnitude of vector v is also equal to 1.

No further normalization is required since the vectors are already of unit length.

In summary, the set {u, v} is an orthonormal set.

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The inequality that represents possible lengths of the third side is 45 ≥  c ≥ 5

The lengths of the two sides are given as:

20 and 25

Let the third side be c.

The triangle inequality theorem states that:

a + b ≥ c

So, we have:

20 + 25 ≥ c

20 + c ≥ 25

25 + c ≥ 20

Evaluate the inequalities

45 ≥ c

c ≥ 5

c ≥ -5

Remove the negative boundary.

So, we have:

45 ≥ c and c ≥ 5

Rewrite as:

45 ≥  c ≥ 5

Hence, the inequality that represents possible lengths of the third side is 45 ≥  c ≥ 5

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Answer:

Step-by-step explanation:

finding the smallest possible distance from the line to the origin follows as

the normal vector=(-1,-2,1)

using direction vector we need to create the equation of the plane

-1(x-2)-2(y-3)+1(z+7)=0

we get;

-x+2-2y+6+z+7=0

-x-2y+z+13=0

x=2-t; y=2-3t; z=-7+t

on substituting;

-1(2-t)-2(3-2t)+1(-7+t)+13=0

-2+t-6+4t-7+t+13=0

we get;

t=1

so point is(1,1,-6)

distance from point to origin

d=\(\sqrt{(1^2+1^2+(-6)^2)}\)=\(\sqrt{38}\)

therefore

the answer is \(\sqrt{38}\)=6.16

Answer:

–2.4 + 3.2t

Step-by-step explanation:

= –3.6 – 1.9t + 1.2 + 5.1t

= –3.6 + 1.2 – 1.9t + 5.1t

= –2.4 + 3.2t

i hope this helped

Answer:

C. The slope of the line is -½

This is the statement that is NOT true

Step-by-step explanation:

The points on the line raise 1 unit up every 2 units across;

The ratio of rise to run is therefore ½;

This is the same as the slope;

Any right-angle triangles formed with the hypotenuse along the line of the graph will be similar

Answer:

21/3+3(4)

21/3+12

21/15

7/5, 1 & 2/5, or 1.4

Answer:

19

Step-by-step explanation:

s/3+3w

21/3+3x4

7+12

19

Part G

The two angles ABD and DBC form a straight line, so the angles add to 180 degrees.

Let's solve for x.

angle ABD + angle DBC = 180

(0.5x+20) + (2x-10) = 180

2.5x+10 = 180

2.5x = 180-10

2.5x = 170

x = 170/2.5

x = 68

Then we'll use this to find angle ABD

angle ABD = 0.5*x + 20

angle ABD = 0.5*68 + 20

angle ABD = 34 + 20

angle ABD = 54

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

Part H

Use the value of x we found back in part G to find the measure of angle DBC

angle DBC = 2x - 10

angle DBC = 2(68) - 10

angle DBC = 136 - 10

angle DBC = 126

An alternative is to subtract the measure of angle ABD from 180

angle ABD + angle DBC = 180

angle DBC = 180 - (angle ABD)

angle DBC = 180 - 54

angle DBC = 126

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

Part I

This time, the two angles add to 90 degrees as shown by the square corner marker.

(angle XYW) + (angle WYZ) = 90

(1.25x - 10) + (0.75x + 20) = 90

2x + 10 = 90

2x = 90-10

2x = 80

x = 80/2

x = 40

which then leads to,

angle XYW = 1.25*x - 10

angle XYW = 1.25*40 - 10

angle XYW = 50 - 10

angle XYW = 40

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

Part J

We can subtract the result of part I from 90 degrees to get the answer

angle WYZ = 90 - (angle XYW)

angle WYZ = 90 - 40

angle WYZ = 50

Or we could plug the x value x = 40 into the expression for angle WYZ

angle WYZ = 0.75*x + 20

angle WYZ = 0.75*40 + 20

angle WYZ = 30 + 20

angle WYZ = 50

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

Summary:

The answers we found were

Answer:

G. m∠ABD = 54°

H. m∠DBC = 126°

I. m∠XYW = 40°

J. m∠WYZ = 50°

Step-by-step explanation:

∠ABD and ∠DBC are supplementary angles. This means their angles have a sum of 180°.

\(\frac{1}{2}x+20+2x-10=180\\\frac{5}{2}x+10=180\\\frac{5}{2}x=170\\x=68\)

m∠ABD = 1/2(68) + 20 = 34 + 20 = 54

m∠DBC = 2(68) - 10 = 136 - 10 = 126

Same concept for ∠XYW and ∠WYZ only this time they are complementary angles. This means their angles have a sum of 90°.

\(1\frac{1}{4}x-10+\frac{3}{4}x+20=90\\2x+10=90\\2x=80\\x=40\)

m∠XYW = 1 1/4(40) - 10 = 50 - 10 = 40

m∠WYZ = 3/4(40) + 20 = 30 + 20 = 50

An equation for C is C = 0.1t + 4.

An interpretation of the slope of the graph is that the total cost of using a computer increases by 0.1 per minute.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 4.5)/(10 - 5)

Slope (m) = 0.5/5

Slope (m) = 0.1

At data point (10, 5) and a slope of 0.1, a linear equation for C can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 0.1(x - 10)

y = 0.1x + 5 - 1

y = 0.1x + 4 ≡ C = 0.1t + 4

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I think C would be for number 11

A is for 12.

x/2 < - 18

The volume of the rectangular prism is 1435.

To find the volume of the rectangular prism, we need to consider the given information that the sum of its volume, total surface area, and the sum of the lengths of all its edges is equal to 2015. By analyzing the properties of a rectangular prism, we can determine the possible combinations of side lengths that satisfy the given condition.

Let's denote the side lengths of the rectangular prism as a, b, and c. The volume of a rectangular prism is given by V = a * b * c, the total surface area is given by A = 2(ab + ac + bc), and the sum of the lengths of all the edges is given by E = 4(a + b + c).

According to the problem statement, we have the equation V + A + E = 2015. Substituting the formulas for V, A, and E, we get:

a * b * c + 2(ab + ac + bc) + 4(a + b + c) = 2015.

By rearranging the equation, we have:

abc + 2ab + 2ac + 2bc + 4a + 4b + 4c = 2015.

Factoring out common terms, we get:

(a + 2)(b + 2)(c + 2) = 2015 + 8 = 2023.

Now, we need to analyze the factors of 2023 to find the possible combinations of side lengths. The factors of 2023 are 1, 7, 17, and 119. We can write (a + 2), (b + 2), and (c + 2) as these factors.

By examining the factors, we find that the combination (a + 2) = 1, (b + 2) = 7, and (c + 2) = 289 satisfies the condition. Solving these equations, we get a = -1, b = 5, and c = 287.

Since the lengths of a rectangular prism cannot be negative, we discard the solution with a = -1. Thus, the valid solution is a = 1, b = 5, and c = 287.

Finally, we can calculate the volume using the formula V = a * b * c:

V = 1 * 5 * 287 = 1435.

Therefore, the volume of the rectangular prism is 1435.

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Answer:

7.76

Step-by-step explanation:

0.22×20=4.4

3.36(base amount ,average of the others)+4.4=7.76

The estimated quotient is $20, which corresponds to option D in the given choices. Thus, Rose estimated that she spent $20 per person on gifts.

Compatible numbers are numbers that are close in value and can be easily divided or multiplied mentally. These numbers are used to make estimation in mathematical calculations easier and quicker. By rounding numbers to compatible numbers, calculations become simpler, and  errors are minimized.

For example, if you need to divide 26 by 5, you can use compatible numbers by rounding 26 to 25 and 5 to 4. Then, you can easily divide 25 by 4 to get an estimate of the quotient as 6.25. Compatible numbers can also be used in multiplication, addition, and subtraction.

Using compatible numbers is particularly helpful when performing mental calculations or when there is no calculator available.

To estimate the quotient of 420 divided by 21 using compatible numbers, we can round 420 to 400 and 21 to 20. Then, we can divide 400 by 20 to get an estimate of the quotient:

420 ≈ 400

21 ≈ 20

400 ÷ 20 = 20

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Answer:

23

Step-by-step explanation:

divide -4 by -44 and you get 11, add 12 because 12 was taken away and you get 23. 11+12=23 23-12=11

There are 168 black cubes in the arranagement.

A cube has 6 faces. Each face of the cube consists of 25 white cubes and 24 black cubes.

To get the number of black cubes in the arrangement, we will use the equation below;

Hence there are 168 black cubes in the arrangement.

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Step-by-step explanation:

=2(6×+7)(7×-4)

=2(+42)(-32)

=2×+42×-32

=84×-32

=-2688

We need to know about the concept of compound interest to solve the given problem. The minimum interest rate that Harry needs to meet his need is 11.4%

Compound interest can be described as the interest that you earn on both the principal amount and the interest earned. In this question it is said that the bank offers annual interest compounded monthly, we will be using a formula to solve this problem. Since Harry has 21350 EUR we will take that as the principal amount and the minimum amount that he needs is 30000 EUR we will consider this to be the final amount at the end of 3 years. We need to find out the rate of interest that the bank offers.

A=P\((1+\frac{r}{12} )^{12t}\) where A is amount, P is principal, r is the rate of interest and t is time period.

P=21350 EUR

A=30000 EUR

t=3

30000=21350\((1+\frac{r}{12}) ^{36}\)

\(\frac{600}{427} =(1+\frac{r}{12}) ^{36}\)

1+\(\frac{r}{12}\)=1.00949

r/12=0.00949

r=0.1139

r=11.4%

Therefore we found that the minimum rate of interest Harry requires to meet his needs is 11.4%

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Given

|x+1|-4

Answer

Domain = all real numbers

Range

After solving the quadratic equation, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

Let's assume that one leg of the right triangle is x units. According to the problem, the other leg is 4 more than twice the length of x, which can be represented as 2x + 4 units.

Using the Pythagorean theorem, we can set up the equation:

\(x^2 + (2x + 4)^2 = 26^2\)

Expanding and simplifying the equation:

\(x^2 + 4x^2 + 16x + 16 = 676\)

\(5x^2 + 16x - 660 = 0\)

We can now solve this quadratic equation to find the value of x. By summing the lengths of the legs (x + 2x + 4), we can determine the final answer.

After solving the quadratic equation, we find two possible solutions: x = 11 and x = -12. Since the lengths of the sides cannot be negative, we consider x = 11 as the valid solution.

Therefore, the sum of the lengths of the legs is 11 + (2 x 11 + 4) = 11 + 26 = 37 units.

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Answer:

x = 5

Step-by-step explanation:

So the perimeter of a square is 4 times the side length.

4 (x+3) = 32 is the equation we can make out with the given information.

Solve for x:

Distribute the 4 to the terms inside the parenthesis;  4x + 12 = 32

Subtract 12 from both sides;  4x = 20

Divide both sides by 4;  x = 5

By isolating x, we get 5 as the value of x.

Answer: a

Step-by-step explanation:

The sensitivity of the pregnancy test is 95% and the specificity is 99%. Given an anticipated 10% pregnancy rate among women using the test, the positive predictive value (PV+) of the test can be determined.

The sensitivity of a test refers to its ability to correctly identify positive cases, while the specificity measures its ability to correctly identify negative cases. In this case, out of the 100 known pregnant women, the test correctly identified 95 as positive, resulting in a sensitivity of 95%. Similarly, out of the 100 known non-pregnant women, the test correctly identified 99 as negative, giving it a specificity of 99%.

To determine the positive predictive value (PV+) of the test, we need to consider the anticipated pregnancy rate among women who will use the test. If 10% of the women who use the test are expected to be pregnant, we can calculate the PV+ using the following formula:

PV+ = (Sensitivity × Prevalence) / (Sensitivity × Prevalence + (1 - Specificity) × (1 - Prevalence))

Substituting the given values, we get:

PV+ = (0.95 × 0.1) / (0.95 × 0.1 + 0.01 × 0.9)

PV+ = 0.095 / (0.095 + 0.009)

PV+ = 0.91

Therefore, the positive predictive value (PV+) of the pregnancy test is approximately 91%.

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Answer:

Step-by-step explanation:

pues supongo que tuviste que traducirlo y no te sirvio de nada la respuesta pero no se nada B 5-8 esa creo yo la verdad

Answer:

Step-by-step explanation:

6

Answer:

0.29 as a percentage is the same as 29%

Step-by-step explanation:

it’s going to be 29% because you just pretend that there isn’t a 0. In front of the 29 and you have 29%.

The decimal number 0.29 is equivalent to 29% when expressed as a percentage.

Given decimal is 0.29.

To convert a decimal number to a percentage, multiply it by 100 and add the percentage symbol (%).

In this case, to convert 0.29 to a percentage

= 0.29 x 100

= 29

Therefore, 0.29 is equivalent to 29% as a percentage.

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Answer:

exponent

Step-by-step explanation:

Answer:

X= 2

y= -3

Step-by-step explanation

Answer:

Step-by-step explanation:

x intercept

The x intercept happens when y = 0

3x - 2y = 6

y = 0

3x = 6

x = 6/3

x = 2

x intercept = 2,0

The y intercept happens when x = 0

-2y = 6

y = 6/-2

y = -3

y intercept = 0,-3

Step-by-step explanation:

For parking, they spent 5$

For student ticket, they spent 8$ (as only Bella is student)

For Non-student ticket, they spent (16*3 = 48$) (as two parents i.e. Mom and Dad plus a grandmother)

Together they spent=

5$+8$+48$

= 61$

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