Daniel is a very good television salesperson. His annual sales average at $187,400. His commission on sales is 30% and his annual base salary is $40,000. On average what is his annual gross income?

Answer:

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

Rewrite expression with bases of 4.

[tex]\sf{4^{\frac{3}{4} }} \times \sf({4^\frac{1}{2} )^x =(4^2)^{\frac{2}{5} }[/tex]

Apply law of exponents, when bases are same for exponents in multiplication, add the exponents. When a base with an exponent has a whole exponent, then multiply the two exponents.

[tex]\sf{4^{\frac{3}{4} }} \times \sf{4^{\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

[tex]\sf{4^{\frac{3}{4} +\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

Cancel same bases.

[tex]\sf \frac{3}{4} +\frac{1}{2} x=\frac{4}{5}[/tex]

Subtract 3/4 from both sides.

[tex]\sf \frac{1}{2} x=\frac{1}{20}[/tex]

Multiply both sides by 2.

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

2^{2*3/4} × 2^{x}=2^{4×2/5}

2^{3/2} × 2^{x}= 2^{8/5}

2^{3/2+x}=2^{8/5}

equate powers

{3+2x}/2= 2^2

5{3+2x}= 2{8}

15+10x=16

collect like terms

10x=16-15

10x=1

divide both sides by 10

x=1/10

x=0.1

Greetings from Brasil...

Using Cossine we will get the length L of ladder

COS 35 = 5/L

Answer:

48cm²

Step-by-step explanation:

PQ=(24-5-5)/2=7

This means PR is 14 and US is 10.

The height of the parallelogram is base times height, so 28/7=4

Now we just look at it as one big parallelogram.

4(14+10)/2=48 cm²

Answer:

i need help this too

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

x = 5

Now, let's find the value of C

[tex]c = 3x - 2[/tex]

plug the value of x

[tex] = 3 \times 5 - 2[/tex]

Multiply the numbers

[tex] = 15 - 2[/tex]

Calculate the difference

[tex] = 13[/tex]

Hope this helps..

Best regards!!

Area of a triangle is 1/2 x base x height.

The graphed triangle has height of 2 and base of 2.

Area = /2 x 2 x 2 = 2 square units.

The triangle gets enlarged by a scale factor of 2, so the new height would be 2 x 2 = 4 and the new base would be 2 x 2 = 4

Area of enlarged triangle = 1/2 x 4 x 4 = 8 square units.

The answer is C) 8

Answer:

             [tex]\bold{A_{_{\Delta XYZ}}=927.5\ cm^2}[/tex]

Step-by-step explanation:

m∠Z = 180° - 118° - 28° = 34°

[tex]\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\[/tex]

[tex]\dfrac{\overline{XY}}{\sin Z}=\dfrac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\dfrac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=\dfrac{42}{0.4695}\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_{\Delta XYZ}}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_{\Delta XYZ}}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5[/tex]

Answer:

The correct option is;

B. The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy

Step-by-step explanation:

The given requirements are;

Volume of air and water to be filtered by the robot = 343 liters

The amount of energy consumed by the robot < 49 joules

The number of minutes the robot filters air and water to filter more than 343 liters = 12A + 8W > 343

The number of minutes the robot filters air and with less than 49 Joule of energy = 3A + 4W < 49

Given that filtering air takes 20 minutes, filtering water takes 15 minutes, we have;

To filter more than 343 liters, we have

12*20 + 8*15 = 360 > 343

The robot meets the amount of air and water requirement

To filter with less than 49 joules we have

3*20 + 4*15 = 120 > 49

Therefore, the robot does not meet the energy requirement

The correct option is the robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.

Answer: sample space

Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] {(4 - 2)}^{3} - 3 \times 4[/tex]

Subtract the numbers

[tex] = {(2)}^{3 } - 3 \times 4[/tex]

Multiply the numbers

[tex] = {(2)}^{3} - 12[/tex]

Evaluate the power

[tex] = 8 - 12[/tex]

Calculate the difference

[tex] = - 4[/tex]

Hope this helps..

Best regards!!

Answer:

[tex]\boxed{-4}[/tex]

Step-by-step explanation:

[tex](4-2)^3-3 \times 4[/tex]

Brackets or parenthesis are to be evaluated first. Subtract the numbers in the brackets.

[tex](2)^3-3 \times 4[/tex]

Evaluate the power or exponent.

[tex]8-3 \times 4[/tex]

Multiply the numbers.

[tex]8-12[/tex]

Finally, subtract the numbers.

[tex]=-4[/tex]

Answer:

0.5645

Step-by-step explanation:

De la pregunta anterior, se nos dan los siguientes valores para el equipo de Ludlow

Probabilidad de jugar de noche = 70% = 0.7

Probabilidad de ganar en la noche = 50% = 0.5

Probabilidad de jugar durante el día = 30% = 0.3

Probabilidad de ganar durante el día = 90% = 0.9

Probabilidad de que cuando ganaron ayer, el juego se jugó por la noche =

(Probabilidad de jugar de noche × Probabilidad de ganar de noche) ÷ [(Probabilidad de jugar de noche × Probabilidad de ganar de noche) + (Probabilidad de jugar de día × Probabilidad de ganar de día)]

Probabilidad de que cuando ganaron ayer, el juego se jugó de noche = (0.5 × 0.7) ÷ (0.5 × 0.7) + (0.9 × 0.3)

= 0.35 ÷ 0.35 + 0.27

= 0.35 ÷ 0.62

= 0.5645

La probabilidad de que el partido se haya jugado de noche = 0.5645

Answer:

We could rewrite 7/2 as 7a + 2

Step-by-step explanation:

Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.

Answer:

30.045

Step-by-step explanation:

the length of rectangle=140 which is also the diameter of circle

R=d/2=140/2=70 ( which is the width of rectangle)

perimeter of rectangle=2l+2w=140+280=420

perimeter of semicircle=πr+d=70π+140=359.911

the difference between two perimeter

(perimeter of rectangle- perimeter of semi circle) =

420-359.911=60.089

since only one shaded area :

60.089/2=30.0445 close to 30.045

D. The line is perpendicular to the plane determined by the two lines.

Remember how you get to 3D space?

You take one axis called x and perpendicularly intersect it with y axis and you get a 2D plane. Now take a 2D plane and perpendicularly intersect it with an axis z and you get 3D euclidean space.

Hope this helps.

Answer:

10.5 cm^2

Step-by-step explanation:

Since we have two sides and the angle between those sides, we can use the alternative area formula:

[tex]A=\frac{1}{2}ab\sin(C)[/tex]

a and b are the two sides while C is the angle in between the two sides.

Plug in the numbers:

[tex]A=\frac{1}{2}(7)(6)\sin(150)[/tex]

Recall the unit circle. Sin(150) is 1/2.

[tex]A=21(\frac{1}{2})[/tex]

[tex]A=21/2=10.5cm^2[/tex]

Answer:

45.

Step-by-step explanation:

100% of a number is the number itself. So, 100% of 45 is 45.

Hope this helps!

Answer:it’s 45

Step-by-step explanation:It’s just the whole number nothing less:)

Answer:

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Step-by-step explanation:

b=7x

sum of straight angle :=180

isoceles traingle = 2 sides are equal, and two angles are equal

b+a=180

7x+a=180

sum of traingle =180

2a+c=180

2a+2x=180  first equation

7x+a=180    second equation

solve by elimination ( multiply second equation by 2)

2a+2x=180

2a+14x=360 ( subtract)

2a+2x-2a-14x=180-360

-12x=-180

x=-180/12=

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

O B. 17 units

Step-by-step explanation:

The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:

[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]

The length of the chord is 17 units.

Answer:

The answer is 17 units :D

Step-by-step explanation:

Answer:

18.5

Step-by-step explanation:

In the above question, we are given the following values

Cumulative probability ( confidence interval) = 0.95 = 95%

Mean = 10.5

Standard deviation = 4.10

We are asked to find the value of x.

To solve for x , we would be using the z score formula.

z score = (x-μ)/σ,

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z score was not given in the question, but we have our cumulative probability as 95%(0.95).

Using the appropriate table,

the z score for 95% confidence is z = 1.96.

Therefore,

z score = (x-μ)/σ,

1.96 = x - 10.5/4.10

Cross multiply

1.96×4.10 = x - 10.5

x = (1.96 × 4.10) + 10.5

x = 8.036 + 10.5

x = 18.536

Approximately to 1 decimal place

x = 18.5

Answer:

Step-by-step explanation:

can you at least telllus what is in the drop box

Answer:

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Step-by-step explanation:

Answer:

2,666.67 L of water

Step-by-step explanation:

Solve for W:

1) 3200 = 2400 + 0.3w

2) 800 = 0.3w

Divide both sides by 0.3 to get the variable alone

3) (800)/0.3 = (0.3w)/0.3

4) w = 2,666.67 L

Answer:

a   1 : 5

Step-by-step explanation:

Blue mables: 3

green and red marbles: 8 + 7 = 15

then, the radio blue:(green+red) is:

3 : 15

simplified unit rate is:

3/3 = 1

15/3 = 5

then:

3:15

is equal to:

1:5

Answer:

a   1 : 5

Answer:

1. True

2. False.

3. True.

Step-by-step explanation:

1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).

Hence, for continuous probability distribution: probability = area.

2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.

Hence, it cannot be computed.

3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.

Hence, it can be computed.

Answer:

855.298 m^3

Step-by-step explanation:

The volume of a cylinder equation is piR^2H.

So pi5.5^2×9

855.298 m^3

Answer:

B

Step-by-step explanation:

common difference is 3

explicit formula is

first term + ( n-1 ) * common difference

= -7 + ( n-1) * 3

Answer:

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Step-by-step explanation:

As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.

Given:

Height of cylinder, [tex]h_1[/tex] = 15 cm

Diameter of cylinder/ cone, D = 26 cm

Slant height of cone, l = 20 cm

Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]

Here,

[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]

To find the Height of Cylinder, we can use the following formula:

[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]

Now, putting the values to find the volume of container:

[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]

Converting [tex]cm^{3 }[/tex] to litres:

[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]

[tex]\approx[/tex] 11 litres of water will fit inside the container.