⁰which of the following is the volume of a hemisphere with a radius of 8 inches?
Answers
The general expression for the volume of hemisphere is :
[tex]\text{ Volume = }\frac{2}{3}\Pi\text{ }\times radius^3\text{ }^{}^{}[/tex]In the given question we have radius = 8 inches
Substitute the value of r = 8 in the expression for the volume of hemisphere :
[tex]\begin{gathered} \text{ Volume = }\frac{2}{3}\Pi\text{ }\times radius^3\text{ }^{} \\ \text{Volume}=\frac{2}{3}\times3.14\times8^3 \\ \text{Volume =}1071.78666 \\ Volume\text{ = 1071.70 inches cubed} \end{gathered}[/tex]B) 1071.79 inches cube
Answer
Related Questions
A polynomial P is given. P(x) = x3 + 3x2 + 6x(a) Find all zeros of P, real and complex.x = (b) Factor P completely.P(x) =
Answers
P(x) is defined by the expression
[tex]P(x)=x^3+3x^2+6x[/tex]Note
[tex]x^3+3x^2+6x=x(x^2+3x+6)\text{ }[/tex]Therefore, one solution is 0.
The other two solutions come from
[tex]x^2+3x+6=0[/tex]Apply the general solution in order to find complex solutions
[tex]\frac{-3\pm\sqrt{3^2-4(1)(6)}}{2(1)}=\frac{-3\pm\sqrt{-15}}{2}[/tex]The solutions are
[tex]0,\frac{-3+i\sqrt{15}\text{ }}{2},\frac{-3-i\sqrt{15}}{2}[/tex]We calculate the factor from the solutions, like this
[tex]x=\frac{-3+i\sqrt{15}}{2}\Rightarrow x+\frac{3}{2}-\frac{i\sqrt{15}}{2}=0[/tex][tex]x=\frac{-3-i\sqrt{15}}{2}\Rightarrow x+\frac{3}{2}+\frac{i\sqrt{15}}{2}=0[/tex]The factor is
[tex]P(x)=x(x+\frac{3}{2}-\frac{i\sqrt{15}}{2})(x+\frac{3}{2}+\frac{i\sqrt{15}}{2})[/tex]If you make $13.00/hour at your job and you work on average 35 hours a week, how much do you bring home if you get $80 taken out in taxes????
Answers
If you make $13/ hour and you work 35 hours, you make:
[tex]13\cdot35\text{ = \$455}[/tex]Then, you substract the $80 in taxes:
[tex]455-80\text{ = \$375}[/tex]So in total, you should bring home $375
Use the law of sines Find each missing side or angle
Answers
The law of sine states that the ratio of Sine A and side a is just equal to the ratio of Sine B and side b which is also equal to the ratio of Sine C and side c. In formula, we have:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]where the big letter A, B, C are the angles and the small letters are the side opposite of the angle.
In our triangle, we have angle 19 and its opposite side is "x" whereas the angle opposite of the side that has a length of 32 units is unknown.
To solve the unknown angle, we know that the total measure of the angle in a triangle is 180 degrees. Therefore, the measure of the missing angle is 180 - 19 - 26 = 135 degrees.
So, going back to the law of sine, we have:
[tex]\begin{gathered} \frac{\sin19}{x}=\frac{\sin 135}{32} \\ \text{Cross multiply.} \\ 32\sin 19=x\sin 135 \\ \text{Divide both sides by sin 135.} \\ \frac{32\sin 19}{\sin 135}=\frac{x\sin 135}{\sin 135} \\ \frac{32\sin 19}{\sin 135}=x \\ \frac{10.41818094}{0.7071067812}=x \\ 14.73\approx x \end{gathered}[/tex]Therefore, the measure of the side x is approximately 14.73 units.
To solve the length of the other side, say y, the side opposite angle 26, we can make use of the law of sine again.
[tex]\begin{gathered} \frac{\sin135}{32}=\frac{\sin 26}{y} \\ y\sin 135=32\sin 26 \\ y=\frac{32\sin 26}{\sin 135} \\ y=\frac{14.0278767}{0.7071067812} \\ y\approx19.84 \end{gathered}[/tex]The length of the other missing side opposite angle 26 is approximately 19.84 units.
Answer:
14.7
Step-by-step explanation:
yes
What is the answer for this question? Why would it be helpful to rewrite the equation that way?
Answers
To solve the equation for "x", we will use operations in both sides of the equation.
[tex]3x+5y=500[/tex]First, we already have the "x" in the left side, but there is also a term with "y", so let's put it to the right side.
to do this, we can substract "5y" in both sides:
[tex]\begin{gathered} 3x+5y-5y=500-5y \\ 3x=500-5y \end{gathered}[/tex]Now, we just need to pass the "3" to the other side, which we can do by dividing both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{500-5y}{3} \\ x=\frac{500}{3}-\frac{5}{3}y \end{gathered}[/tex]Tha is the equation solved for "x".
This way of writing the equation can be usefull if we want to calculate "x" for a given "y" value, that is, if we know the number of adult tickets sold, we can substitute it into the equation in this form and just evaluate the right part to obtain the "x" value.
Jada has 4 meters of ribbon. How many pieces of ribbon of length 1/3 meter can she cut from it. Draw a diagram to illustrate your solutions.
Answers
She can cut twelve 1/3 meters from 4 meters.
The diagram is shown in the explanation below.
Explanation:Parameters:
Total length of ribbon = 4 meters
Let x represent the number of 1/3 meters she can cut, then
[tex]\begin{gathered} \frac{1}{3}x=4 \\ x=4\times3=12 \end{gathered}[/tex]She can cut twelve 1/3 meters from 4 meters.
This is illustrated in the diagram below:
What the percent 7/800
Answers
You have to divide 7 by 800:
[tex]\frac{7}{800}=0.00875[/tex]Now multiply by 100
[tex]0.00875*100=0.875\%[/tex]The answer is 0.875%
2Select all values of x that make the inequality -x + 8 >11 true.A-2B-6С-4D1E3F.-3
Answers
To solve this problem, we need to know which values of x would make the inequality -x + 8 > 11 true.
To do this, we will need to solve the equation in terms of x, just like how we normally solve for x in any linear equation.
[tex]-x+8>11[/tex]Using the Addition Property of E
Pre-Calculus_Unit 1_Math_20-21 / 4 of 16 Find the slope of the line determined by the equation 3x +10y = 11 O A. m = -3 OB. m= 3 O C. 3 m=- 10 11 10 Em: -10
Answers
Brook, this is the solution:
Let's find the slope for this equation:
3x + 10y = 11
10y = -3x + 11
Dividing by 10 at both sides:
10y/10 = -3x/10 + 11/10
y = -3x/10 + 11/10
Therefore,
m = -3/10
showing all your work for problem 1 divide simplify and state the domain and problem 2 multiply simplify and state the domain
Answers
The domain of the problem is given as
[tex](-\infty,\text{ 0) U (0, +}\infty)[/tex]Higher Order Thinking Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1. Can their sum equal 1? Can their sum be greater than 1? Explain.
Answers
1) Gathering the data
2) Since we don't know exactly their numerators we can write, for instance, two fractions with the same bottom number and lesser than 1:
[tex]\begin{gathered} \frac{1}{4},\text{ }\frac{3}{4} \\ \frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1 \\ \frac{2}{4}+\frac{3}{4}=\frac{5}{4}=1.25 \\ \frac{1}{5}+\frac{3}{5}=\frac{4}{5}=0.8 \end{gathered}[/tex]2) Hence, we can conclude that the sum can be equal to 1, greater than 1, and lesser than 1. That'll depend on the numerator, and the fractions Leah can pick.
3) So, they can be less, equal to, and greater than 1.
Let f(x) = x² + 11x + 25 Find a so that f(a) = 1
Answers
A=-3
A=-8
Explanation
Step 1
[tex]f(x)=x^2+11x+25[/tex]there is a number A so f(A) =1, then
[tex]\begin{gathered} f(A)=A^2+11A+25 \\ f(A)=1 \\ \text{then} \\ A^2+11A+25=1 \\ A^2+11A+24=0\text{ equation(1)} \end{gathered}[/tex]Step 2
solve using the quadratic equation
[tex]\begin{gathered} \text{for } \\ ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]a)let
a=1
b=11
c=24
the variable is A,
b) replace
[tex]\begin{gathered} A=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ A=\frac{-11\pm\sqrt[]{121^{}-4\cdot1\cdot24}}{2\cdot1} \\ A=\frac{-11\pm\sqrt[]{121^{}-96}}{2} \\ A=\frac{-11\pm\sqrt[]{25}}{2} \\ A_1=\frac{-11+\sqrt[]{25}}{2}=\frac{-11+5}{2}=\frac{-6}{2}=-3 \\ A_1=-3 \\ A_2=\frac{-11-\sqrt[]{25}}{2}=\frac{-11-5}{2}=\frac{-16}{2}=-8 \\ A_2=-8 \end{gathered}[/tex]I hope this helps you
I narrowly answered the first question on my homework but for some reason EF really confuses me.
Answers
Solution
Part 1
For this case we can find DF with the following proportion formula:
[tex]\frac{AC}{AB}=\frac{DF}{DE}[/tex]And replacing we got:
[tex]\frac{4}{2}=\frac{DF}{1.34},DF=2.68[/tex]Part 2
[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]And solving for EF we got:
[tex]EF=1.34\cdot\frac{3}{2}=2.01[/tex]choose the x-intercept and the y-intercept for each equationx+4y=24a (0,4)b (0,6)c (6,0)d (24,0)e (24,6)
Answers
Given:
The equation is x + 4y = 24
Required:
Find the x - intercept and y - intercept?
Explanation:
We know that
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]Where, a is x - intercept
and b is y - intercept
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
Now,
[tex]\begin{gathered} x+4y=24 \\ \frac{x}{24}+\frac{y}{6}=1 \end{gathered}[/tex]From this we can say that x - intercept (24, 0) and y - intercept (0, 6).
Answer:
Hence, (24, 0) and (0, 6) are intercept of given equation.
Mrs. Davis has 20 people in her 6th period class. 12 of the people are boys. What percent of Mrs. Davis's 6th period class are boys? 70% 40% 50% 60%
Answers
Mrs. Davis has 20 people in her 6th period class. 12 of the people are boys. What percent of Mrs. Davis's 6th period class are boys? 70% 40% 50% 60%
we know that
20 people represent 100%
so
Applying proportion
20/100%=12/x
solve for x
x=(100*12)/20
x=60%
therefore
the answer is 60%QuestioA team of physicians is studying a weight-loss pill. They recruited volunteers for a study. The volunteers were in the agegroup of 30 to 35 and were more than 40 pounds overweight. The physicians gave the new weight-loss pill pack to onegroup. The other group received a pill pack that resembled the new weight-loss pill pack but was a placebo. In thedescription of the above situation, determine the experimental group
Answers
The experimental group will be the group who received the new weight-loss pill. This group will be used to identify or estimate the effect of the variable or the ingredient which will cause weight loss.
The other group who received the resemblanced of the new weight-loss pill but placebo will only be used for the comparison effect from the experimental group.
So the answer will be :
1st Option, The group that received the new weight-loss pill pack is the experimental group.
Six times a number is greater than 20 more than that number. What are the possible values of that number?a. n<4b. n>4c. n>20/7d. n<20/7
Answers
Let's call n to the number of interest. The following inequality represents this problem:
6n > 20 + n
Solving for n
6n - n > 20
5n > 20
n > 20/5
n > 4
√10=Rational or Irrational
Answers
Square roots are rational only when has perfect square factors.
√10 = √(2*5) = √2 * √5
2 and 5 are not perfect squares, then √2 and √5 are irrational. In consequence, √10 is also irrational.
What is the value of the expression belowwhen y = 9 and z = 3?10y - 7z
Answers
y= 9 & z = 3
10y - 7z
put y= 9 & z = 3
= 10 (9) - 7(3)
= 90 - 21
= 69
so the answer is 69
not college I misclicked but the question is in pic
Answers
Answer
x = 13.33 units
Explanation
We can easily tell that the small triangle (with sides 6 and 8) is similar to the bigger triangle with sides (6+4 and x).
And the ratio of corresponding sides is the same for two similar triangles.
From the image, we can see that
6 is corresponding to (6 + 4)
8 is corresponding to x
So,
[tex]\begin{gathered} \frac{6}{6+4}=\frac{8}{x} \\ \frac{6}{10}=\frac{8}{x} \end{gathered}[/tex]We can now cross multiply
6x = (8) (10)
6x = 80
Divide both sides by 6
(6x/6) = (80/6)
x = 13.33 units
Hope this Helps!!!
Solve Brain Teaser
Write an expression that has a value of 40 using two operations and each of the numbers 1, 2, 3, 4, and 5 exactly once.
More Rules for Your Expression
You can use parentheses or other grouping symbols.
You can make one of your numbers an exponent.
You can use either operation as many times as you like, but you can use each number only one time in the expression.
Bonus Challenge
This brain teaser has more than one solution. Can you find one more?
Answers
The required expression is given as 2×4×5, this gives the value 40.
Given that,
To write an expression that has a value of 40 using two operations and each of the numbers 1, 2, 3, 4, and 5 exactly once.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
From the multiple iterations, we have to choose appropriate numbers,
first the greatest multiplied value can be calculated by two number is given as,
4 × 5 = 20,
Now we have to determine only one operation.
So when we multiply 20 by 2 we get 40,
So.
40 = 2×4×5
Thus, the required expression is given as 2×4×5, this gives the value 40.
Learn more about simplification here:
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A local bakery, theprice for abughouts for his employeespurchasedAFX) -0.65- 3.5prie for $3.50 and some doudoughnuts 30.05. Each day the manager at the store buyswhich equation represents the total cosa function of the number of doughtswhich equation on where represents the number of tires produced over resismodels the function ?BFX) - 0.65x + 3.5CX-3.5x + 0.85DX) - 3.5x -0.85Aebire manufacturing plant produces soo tires a day on average. If the production ofAFX) - 500 + xB (x) - 500 -Cx) - 500xDX) - 5006.Bushra purchases a car for $12,900. The car will depreciate at a rate of 15% each year,After how many years will the value of the car bethan $3,000?A 6 yearsB 7 yearsC8 yearsD 9 years
Answers
In order to create a function that represents the cost of the manager as a function of the number of doughnuts he buys, we need to multiply the cost of each doughnut ($ 0.85) by the number of employees the manager has and add the value of the pie ($ 3.5). This is done below:
[tex]f(x)\text{ = }0.85\cdot x\text{ + 3.5}[/tex]The correct option is the letter B.
The car starts at $ 12,900 and depreciate at a rate of 15% each year. This means that the value of the car on any given year is ruled by the tollowing expression:
[tex]M\text{ = C}\cdot(1-r)^t[/tex]Where "M" is the value of the car after "t" years, C is the initial value of the car and "r" is the rate at which the car depreciates every year divided by 100. Aplying the data from the problem on the expression gives us:
[tex]3000\text{ = 12900}\cdot(1\text{ - }\frac{15}{100})^t[/tex]We want to solve for the variable "t", because we want to know how many years it'll take until the car reaches the final value of 3000.
[tex]\begin{gathered} 12900\cdot(1\text{ - }\frac{15}{100})^t\text{ = 3000} \\ (1\text{ - }\frac{15}{100})^t\text{ = }\frac{3000}{12900} \\ (1-0.15)^t\text{ = }\frac{30}{129} \\ (0.85)^t\text{ = }\frac{30}{129} \end{gathered}[/tex]We have reached an exponential equation. To solve it we need to aply a logarithm on both sides of the equation.
[tex]\begin{gathered} \ln (0.85^t)\text{ = }\ln (\frac{30}{129}) \\ t\cdot\ln (0.85)\text{ = }ln(30)\text{ - ln(129)} \\ t\cdot(-0.1625)\text{ = }3.4\text{ - 4.86} \\ t\text{ = }\frac{-1.46}{-0.1625}\text{ = 8.98} \end{gathered}[/tex]It'll take approximately 9 years to reach that value. The correct option is the letter "D".
Frank has a circle Garden the area of the garden is 100 ft² what is the approximate distance from the edge of Frank's garden to the center of the garden ? (A = pi r²)
Answers
The area of a cirle is given by
[tex]A=\pi(R^2)\text{ where R is the radius, the distance from the edge/circumference to the centre}[/tex]We seek to find R, so let us make it the subject of the formula;
[tex]R=\sqrt[]{\frac{A}{\pi}}[/tex][tex]\begin{gathered} R=\sqrt[]{\frac{100}{3.142}} \\ R=5.64\approx6ft \end{gathered}[/tex]Therefore, the approximate distance from the edge of Frank's garden to the center of the garden is 6ft
A roll of 50 dimes weighs 4 ounces. Which proportion can be used to find the weight in ounces, w, of 300 dimes?
Answers
50 dimes = 4 ounces
300 dimes = w ounces
[tex]\begin{gathered} \frac{50}{300}=\frac{4}{w} \\ \frac{1}{6}=\frac{4}{w} \\ w=24 \end{gathered}[/tex]300 dimes = 24 ounces
the proportion is 1/6 =4/w
Write the function graphed below in the form g(x)… reference photo
Answers
We will have the following:
First, we can see that the function in the image will have a mother function:
[tex]y=\sqrt[3]{x}[/tex]Where the function has been moved 2 units left, and 2 units down:
[tex]y=\sqrt[3]{x+2}-2[/tex]Now, we known that the function has been expanded on the vertical, so:
[tex]y=a\sqrt[3]{x+2}-2[/tex]Now, we solve for "a" while we replace for a value of the function, we can see that (6, 4) belongs, so:
[tex]\begin{gathered} 4=a\sqrt[3]{6+2}-2\Rightarrow4=a\sqrt[3]{8}-2 \\ \\ \Rightarrow6=2a\Rightarrow a=3 \end{gathered}[/tex]So, the equation of the function will be:
[tex]g(x)=3\sqrt[3]{x+2}-2[/tex]This can be seeing as follows:
7/9 + 2/7pls help me
Answers
We have to sum fractions:
[tex]\frac{7}{9}+\frac{2}{7}=\frac{7\cdot7+2\cdot9}{7\cdot9}=\frac{49+18}{63}=\frac{67}{63}[/tex]Evaluate 0^0.
Provide justifications for your conclusion.
Answers
The power expression 0⁰ leads to an indetermination.
What is the result of 0⁰ according to algebra properties?Let be the power expression 0⁰, whose result has to be found by means of algebra properties, especially those related to operations between powers. First, write the entire expression:
0⁰
Second, use the existence property of additive inverse:
0ⁿ ⁺ ⁽⁻ⁿ⁾, where n is a real number.
Third, use power properties:
0ⁿ · 0⁻ⁿ
0ⁿ · (0ⁿ)⁻¹
0 · 0⁻¹
Fourth, by definition of division:
0 / 0
The term 0 / 0 represents an indetermination.
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You're feeling hungry so you order a 40-piece Chicken Nuggets from McDonalds. It costs $8.99. You have a 10% off coupon, but you also have to pay 10% sales tax. What is the final price? Round your answer to the nearest cent.
Answers
In order to calculate the discount of 10%, we can just multiply the number by 90%, that is, 0.9.
And in order to calculate the increase of 10% by the taxes, we can multiply the number by 110%, that is, 1.1.
So, applying both these percentages together, we have:
[tex]\begin{gathered} \text{Price}=8.99\cdot0.9\cdot1.1 \\ \text{Price}=8.9 \end{gathered}[/tex]So the final price will be $8.90.
$800 is deposited in a bank account which is compounded continuously at 8.5% annual interest rate. The future balance of the accourby the function: A = 800e0.085t. How long will it take for the initial deposit to double? Round off to the nearest tenth of a year.
Answers
Given:
Function :
[tex]A=800e^{0.085t}[/tex]Initial deposit =$800
Annual interest rate =8.5%
[tex]A=A_0e^{rt}[/tex]Where,
[tex]\begin{gathered} A=\text{Amount after t time} \\ A_0=\text{Initial amount} \\ r=\text{interest rate} \\ t=\text{time} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{8.5}{100} \\ r=0.085 \end{gathered}[/tex]When deposit is double of initial deposit .
[tex]\begin{gathered} 2\times800=800e^{0.085t} \\ \frac{2\times800}{800}=e^{0.085t} \\ 2=e^{0.085t} \\ \ln 2=\ln e^{0.085t} \\ 0.085t=0.69314 \\ t=\frac{0.69314}{0.085} \\ t=8.15 \end{gathered}[/tex]So after 8.15 year initial amount will be double.
can you help me with this? i am looking for perimeter and and area
Answers
For this problem, we are given a rectangle with the measurement of its dyagonal and the angle between the dyagonal and the base. We need to determine the perimeter and area for this rectangle.
For this, we need to analyze the right triangle that is formed between the dyagonal, the width and height of the rectangle. This triangle is shown below:
From the image above, we can notice that the height is the opposite side to the known angle. Therefore we can calculate it by using the sine relation on a right triangle.
[tex]\begin{gathered} \sin 29=\frac{\text{ height}}{18} \\ \text{height}=18\cdot\sin 29 \\ \text{height}=18\cdot0.48 \\ \text{height}=8.73 \end{gathered}[/tex]The rectangle's height is equal to 8.73 ft.
On the other hand the width is the adjascent side to the known angle, therefore we can calculate it by using the cossine relation.
[tex]\begin{gathered} \cos 29=\frac{\text{ width}}{18} \\ \text{width}=18\cdot\cos 29 \\ \text{width}=18\cdot0.87 \\ \text{width}=15.74 \end{gathered}[/tex]The rectangle's width is equal to 15.74 ft.
Now we can calculate the perimeter and area for the rectangle.
[tex]\begin{gathered} P=2\cdot(\text{width}+\text{height)} \\ P=2\cdot(15.74+8.73) \\ P=2\cdot24.47 \\ P=48.94\text{ ft} \end{gathered}[/tex]The perimeter for the rectangle is 48.94 ft.
[tex]\begin{gathered} A=\text{width}\cdot\text{height} \\ A=15.74\cdot8.73 \\ A=137.41 \end{gathered}[/tex]The area for the rectangle is 137.41 square ft.
a dime, a nickel, and a penny are each tossed one time. which table shows all the possible ways the coins could land face up, using H for heads and T for tails?
Answers
GIVEN:
We are told that an experiment consists of tossing a dime, a nickel and a penny, each of them once.
Required;
Select which table shows all the possible ways the coins could land face up, using H for heads and T for tails.
Step-by-step solution;
First we consider the entire sample space for the experiment, and that is all the possible outcomes for this experiment. This is shown below;
[tex]HHH,\text{ }HHT,\text{ }HTH,\text{ }THH,\text{ }TTH,\text{ }THT,\text{ }HTT,\text{ }TTT[/tex]The second table shows the possible outcomes whereby all coins lands face up without any outcome of landing tails up, that is TTT. Tables 1, 3 and 4 shows possibilities of having a tails for every throw in one of the outcomes (that is, TTT).
Therefore table 2 is the only set of outcomes where the coins could land face up.
ANSWER:
Table 2 (second option).