Sale price $9,450 sale tax rate 8%

Answer: 39

Step-by-step explanation:

30-8=22

22/2=11

11+2=13

13 times 3 =39

Answer:

1 h with 20 min

Step-by-step explanation:

10-6 = 100-60

= 40, in percentages is 40%, 40% minus of 2 h is...

if 50% minus is 1 h, 40% is 1 h with 20 min or simply...

120 min - 40% = 120 - 40

120 - 40 = 80, 80 min are 1 h and 20 min

Hope this helps

Given data:

Distance: 9/10 mile

Time: 1/6 hour

Part A: The average rate that Cecelia traveled is calculated by dividing the distance into the time

Part B:

The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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We want to know the perimeter and area of a rectangle given that we know where the vertices are.

We will get:

perimeter = 26

area = 42

While you wrote verticals, you wrote points, then I assume that it should say vertices.

The vertices of the rectangle are:

(-3.5, 3), (3.5, 3), (-3.5, -3), and one missing but that is the final one, (3.5, -3).

Note that we have two x-values and two y-values, we can define the length as the difference in the x-values and the width as the difference in the y-values, then we will get:

length = 3.5 - (-3.5) = 7

width = 3 - (-3)  = 6

Now we know the length and width of the rectangle, the perimeter is:

P = 2*(6 + 7) = 26

The area is:

A = 6*7 = 42

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Answer:

x⁰ = 45⁰

Step-by-step explanation:

As it is given that the 2 sides of a triangle are equal, then it is an isosceles triangle.

Now, by applying the Triangle Sum Property,

x⁰ + 90⁰ + 45⁰ = 180⁰

x⁰ = 180⁰ - 135⁰

x⁰ = 45⁰

Hope it helps :)

Answer:

x = 45 degrees

Step-by-step explanation:

A triangle is always 180 degrees. One angle is already labeled 45 degrees, and we can tell this is a right triangle, so the other angle is 90 degrees. Add 45 + 90 to get 135. Then subtract 135 from 180 to get 45, which is the value of the missing angle.

To complete the square is take the second term in the expression, divided it by 2 and then squared it. This will be the number that we have to add to the original expression.

(14/2)^2=49

so, completing the expression:

x^2+14x+49

Then, the new expression can be factored into a single term squared:

x^2+14x+49= (x+7)^2

The number of terminates are 2,384.78.

An exponential function can be used to illustrate the daily growth of termites.

If "t" represents the number of days, then "N" represents the number of termites.

⇒ N = \(1600(1 + 0.042)^{t}\)

Where 0.042 is the decimal form of 4.2%.

Using this formula,

It can be  calculate the number of termites after any number of days t.

For example,

After 10 days, the number of termites would be:

⇒ N = \(1600(1 + 0.042)^{10}\)

⇒ N = \(1600(1.042)^{10}\)

⇒ N ≈ 2,384.78 termites

Hence,

⇒ N =  2,384.78 termites

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Answer:

-55 5/10000

Step-by-step explanation:

We can break each word down. Negative would be the negative sign (-), fifty-five would be 55, and five ten-thousandths would be 5/10000. If we put them together, we would get -55 5/10000, which is the answer.

Answer:

24:5

Step-by-step explanation:

4 yards is 3 feet, so 4*3=12. There are 12 inches in a foot, so 12*12=144. 144:30= 72:15 = 24:5

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

Step-by-step explanation:

The perimeter of the triangle shown is 17x units. The dimensions of the triangle are given in units. Which equation can be used to find the value of x?

7x + 15 + 15 = 17x

30 = 10x

x = 3

--------------------

check

7×3+15+15=17×3

21 + 30 = 51

51=51

the answer is good

Answer:

17x=30+7x

Step-by-step explanation:

Entry ticket = $7

Gift shop money = $g

Maximum to spend = $30

Inequality => 7+g ≤ 30

Hope it helps!

9514 1404 393

Answer:

  3210 = 2·3·5·107

  3528 = 2³·3²·7²

Step-by-step explanation:

Divisibility rules help.

A number is divisible by 2 if it is even.

A number is divisible by 3 if the sum of digits is divisible by 3.

A number is divisible by 5 if it ends in 5 or 0.

A number is divisible by 7 if subtracting twice the 1s digit from the rest of the number results in a number divisible by 7.

  Even, and ends in 0, so is divisible by 2·5

  3210/10 = 321

  Sum of digits is 6, so is divisible by 3

  321/3 = 107

  None of the divisibility rules applies, and √107 ≈ 10.3, so there are no prime factors of 107.

  3210 = 2·3·5·107

__

  Ends in 2 digits divisible by 4, so is divisible by 4

  3528/4 = 882

  Even, so is divisible by 2

  882/2 = 441

  Sum of digits is 9, so is divisible by 9

  441/9 = 49

  This is recognizable as the square of 7.

  3528 = 2³·3²·7²

The solution for the given system of equations is

x = 3

y = -12

What are linear equations in two variables?

Therefore, a linear equation in two variables is any equation that can be written in the form ax + by + c = 0, where a, b, and c are real values, and a and b are not equal to zero.

Given two linear equations of two variables.

y = -4x .....eq 1

6x - y = 30 .....eq 2

We have to solve them using substitution.

Now,

by substituting eq 1 in eq 2,

6x -(-4x) = 30

6x + 4x = 30

10x = 30

x = 3

from eq 1,

y = -4x = -4*3 = -12

Therefore, x = 3 and y = -12

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Answer:

c i think im kinda not smart and its 4 am so

Given parameters:

Actual length = 260m

Drawing length = 286mm

Unknown:

Scale used = ?

Solution:

A scale compares drawing length to ground distance;

                    To find the scale,

Express the two quantities in the same unit;

       actual length  = 260 x 10⁻³m = 0.26mm

  Now;

           drawing length : actual length

                  286mm : 260 x 10⁻³mm

                  divide by 286;

                     1mm on drawing  : 9 x 10⁻⁴mm on map

   or;

                     1mm on drawing is 0.9m on ground

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

Students that are under the age of 15 and travel to school in a car has the lowest joint frequency.

Joint frequency are the frequencies of two values that occur jointly in a two way frequency table.

Number of students under age 15 who walk/bike = 152 - 65 = 87

Number of students of age 15 and above who walk/bike = 65

Total number of students who walk/bike = 152

Number of students under age 15 who take bus = 60

Number of students of age 15 and above who take bus = 110 - 60 = 50

Total students who take bus = 110

Number of students of age 15 and above who take car = 195 - (65 + 50)

                                                                                            = 80

Number of students under age 15 who take car = 100 - 80 = 20

Total number of students under age 15 = 362 - 195 = 167

Total number of students of age 15 and above = 195

Total number of students = 362

The lowest value is for the students under the age of 15 who take car.

Hence the lowest joint frequency is for the students under the age of 15 who take car.

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Answer:

14 = n - 6

Step-by-step explanation:

"Is" indicates equal to. "Less" means subtract.

The equation that shows this relationship would be; 14 = n - 6.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

We have been given a statement "Fourteen is 6 less a number (n)."

So  here, "Is" indicates equal to sign. "Less" means subtract.

The equation form would be;

14 = n - 6

The equation that shows this relationship would be; 14 = n - 6.

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Answer:

DAB = BCD

Step-by-step explanation:

DAC = BAC = 90 degrees and DAB = ABC = 90 degrees don't work because they're both equilateral triangles and don't have a right angle that would equal 90. DAB = ABC are clearly not congruent so the answer is DAB = BCD. Also DAB = BCD share the same midsection line.

Answer:

B, C

Step-by-step explanation:

x^2 = 5x - 6

x = 2 or x = 3

The probability that at most 2 of the next 10 callers have to wait more than 8 minutes is the sum of the probabilities of 0, 1, or 2 callers having to wait for more than 8 minutes which is 0.810

The probability that at most 2 of the next 10 callers having to wait can be defined using the expression :

P(X ≤ 2) = P(0) + P(1) + P(2)

Using the individual probabilities given by the histogram attached :

P(X ≤ 2) = 0.181 + 0.345 + 0.284

P(X ≤ 2) = 0.810

Therefore, the probability that at most 2 callers have to wait more than 8 minutes is 0.810

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

X=1

Step-by-step explanation: