Answers
From the figure, the radius of the sphere is:
[tex]r=1\text{ in}[/tex]The volume of the sphere is given by the formula:
[tex]V=\frac{4}{3}\pi r³[/tex]Using the value of the radius:
[tex]\begin{gathered} V=\frac{4}{3}\pi(1)³ \\ \\ \therefore V=\frac{4\pi}{3}\text{ in^^b3} \end{gathered}[/tex]Approximating to the nearest cubic inch:
[tex]\therefore V\approx4\text{ in^^b3}[/tex]ther
Related Questions
a package of 8 count AA batteries costs 6.40 a package of 20 count AA batteries costs 15.80 which statement about the unit price is true?the 20 count pack of AA batreries has a lower unit price of 0.80 per batterythe 8 count pack of AA batteries has a lower unit price 0.79 per batterythe 8 count pack of AA batteries has a low unit price of .80 per batterythe 20 count pack of AA batteries has a lower unit price of .79 per battery
Answers
Notice that for the $6.40 package each battery costs:
[tex]\frac{6.40}{8}=0.80.[/tex]For the $15.80 package each battery costs:
[tex]\frac{15.80}{20}=0.79.[/tex]Therefore, the 20 count pack of AA batteries has a lower unit price of $0.79 per battery.
Answer: Last option.
Gary has read 30 pages of his book. Each day he wants to read 15 pages until he finishes the book which has a total of 180 pages. Write an equation to represent the situation
Answers
ANSWER
30 + 15x = 180
EXPLANATION
We have that Gary has read 30 pages of his book.
He wants to read 15 pages every day till he finishes the 180 pages.
Let the number of days it will take him be x.
This means that after reading 15 pages for x days, he will have read:
15 * x = 15x
Therefore, the total number of pages he will have read (180) will be:
30 + 15x = 180
That is the equation that represents the situation.
find the area of figure using 3.14 for pi. round your answer to nearest tenth if necessary.
Answers
Given a figure to find the area of the figure.
The given figure is the combination of two triangles and a semi-circle.
Here the radius and the base of the triangle is 10 yd and the height of the triangle is 21 yd. So, the area of the figure is;
[tex]\begin{gathered} A=2\times\frac{1}{2}\times\text{base}\times\text{height}+\frac{\pi r^2}{2} \\ =10\times21+\frac{3.14\times10^2}{2} \\ =210+\frac{314}{2} \\ =210+157 \\ =367 \end{gathered}[/tex]Thus, the area of the figure is 367 yd^2.
1. Input, X 9753 1 Output, y 1 2 2 3 4 Function - Yes or no
Answers
before we can dtermone whether it is a function, there must be a relationship between X and y i.e they must have a constannt of proportionality as shown:
From the table:
when x = 9, y = 1
when x = 7, y = 2
when x = 5, y = 2
when x = 3, y = 3
when x = 1, y = 4
let us determine the constant of proportionality from the given values as shown:
k = y2-y1/x2-x1
when x = 9, y = 1
when x = 7, y = 2
k = 2-1/7-9
k = 1/-2
k = -1/2
Also
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Also;
when x = 5, y = 2
when x = 3, y = 3
k = 3-2/3-5
k = 1/-2
k = -1/2
Since all the constant of proportionality are the same;
Hence y = kx
y = -1/2 x
This shows that the tabke is a function and X is directly proportional to y. hence the answer is YES, it is function
Reason
For every x value there is a unique y value, so the x value “input” cannot be repeated. If there are two like x values, there will be two points on your graph that will not pass the vertical line test. The vertical line test is used to determine if a set is a function or not.
See attachment for example.
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 8". Find P(A). Outcome Probability 1 0.12 2 0.11 3 0.4 4 0.02 5 0.04 6 0.17 7 0.02 00 0.09 9 0.03
Answers
We want to calculate the probability of this event A: "the outcome is less than 8". To calculate this probability, we should first note that we have a total of 9 outcomes. So, we will first identify out of this outcomes cause the event A to happen.
Since the event A is saying that the outcome is less than 8, then the outcomes that would make the event A to happen would be the numbers from 1 to 7. However, to calculate this probabilty, we will use this property of probability.
Given an event A, we have the
What is 150% of 38.
Answers
We are asked to find 150% of 38
Step 1:
Convert the 150% to decimal by removing the % sign which means dividing by 100.
150/100 = 1.5
Step 2:
Now simply multiply the decimal percentage with the number 38
1.5×38 = 57
Therefore, 150% of 38 is found to be 57
the area of a triangular wedge is 90 square inches the height is 18in what is the base
Answers
it is given that,
the height of the wedge is h = 18 in
the area of the wedge is A = 90 square in.
we know that the area of a triangle is
A = 1/2 x base x height
put values,
90 = 1/2 x base x 18
90/18 = 1/2 x base
5 = 1/2 x base
base = 5 x 2
base = 10 inches,
thus, the base of the wedge is 10 inches,
a man pushes a car with a force of 127.5n along a straight horizontal road.he manages to increase the speed of the car from 1 m/s to 2.8 m/s in 12 seconds. find the mass of the car. figure out acceleration first.
Answers
In order to determine the mass of the car, you first calculate the acceleration of the car, by using the following formula:
[tex]a=\frac{v_2-v_1}{\Delta t}[/tex]where:
v2: final speed of the car = 2.8 m/s
v1: initial speed of the car = 1 m/s
Δt: time interval = 12 s
You replace the previoues values into th formula for the acceleration:
[tex]a=\frac{2.8m/s-1.0m/s}{12s}=0.15\frac{m}{s^2}[/tex]Next, you the Newton's second law to find the mass of the car. You proceed as follow;
[tex]F=ma[/tex]where:
m: mass of the car = ?
a: acceleration of the car = 0.15m/s²
F: force exerted on the car by the man = 127.5N
You solve for m in the formula for F, and you replace the values of the other parameters to obtain m, just as follow:
[tex]m=\frac{F}{a}=\frac{127.5N}{0.15m/s^2}=850\operatorname{kg}[/tex]Hence, the mass of the car is 850kg
Hello, can you please help me solve this question ASAP!!!
Answers
SOLUTION:
Step 1:
In this question, we have that:
Step 2:
Part A:
We are meant to show that the equation:
[tex]5sinx=1+2cos^2x[/tex]can be written in the form
[tex]2sin^2\text{x + 5 sin x - 3=0}[/tex]Proof:
[tex]\begin{gathered} \text{5 sin x = 1 + 2 cos }^2x\text{ } \\ \text{But cos}^2x+sin^2x\text{ = 1} \\ \text{Then,} \\ \cos ^2x=1-sin^2x\text{ } \\ \text{Hence,} \\ 5sinx=1+2(1-sin^2x_{}) \\ 5sinx=1+2-2sin^2x \\ 5sinx=3-2sin^2x \end{gathered}[/tex]Re-arranging, we have that:
[tex]2sin^2x\text{ + 5 sin x - 3 = 0 }[/tex]Part B:
b) Hence, solve for x in the interval:
[tex]0\text{ }\leq\text{ x }\leq\text{ 2}\pi[/tex]HighByte Entertainment sells four types of products: video games, DVDs, CDs, and radios. The numbers sold for 2020 and 2021 are shown in the double bargraph below. Use this graph to answer the questions.
Answers
Solution
Use this graph to answer the questions below:
The numbers sold for 2020 and 2021 are shown in the double bar above
1. The number of radio sold in 2021 = 440
2. Which products sold more in 2021 than in 2020 :
The only products that sold more in 2021 than in 2020 is video games
3. Which products sold the least over the two years
The products that sold the least = DVDS
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $240 and first class tickets for $1040. She used her total budget for airfare for the trip, which was $4000
. How many first class tickets did she buy? How many coach tickets did she buy?
Answers
Sarah bought 8 first class tickets and she buy 2 coach ticket .
In the question ,
it is given that
total number of people including Sarah = 10 people .
let the number of first class ticket = f
let the number of coach tickets = c
So , the equation is f + c = 10
f = 10 - c
the cost for first class tickets = $240
the cost for "f" first class tickets = 240f
the cost for coach tickets = $1040
the cost for "c" coach tickets = 1040c
total budget is $4000 .
So , the equation is 240f + 1040c = 4000
On substituting f = 10 - c , we get
240(10 - c) + 1040c = 4000
2400 - 240c + 1040c = 4000
1040c - 240c = 4000 - 2400
800c = 1600
c = 1600/800
c = 2
and f = 10 - 2 = 8 .
Therefore , Sarah but 8 first class tickets and she buy 2 coach ticket .
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mathematics assignment
Answers
Examining the function the graph that is correct is the graph in option C
What is graph ?A graph is a representation of data using accepted means of presentation.
The graph used in the question is in cartesian coordinate and it a parabolic graph
How to find the correct graphThe given data is h(x) = -x² - 4
Examining the given function
The term -x² is a negative term hence the graph opens downwards
The value of h(x) when x = 0 is -4. Therefore the graph will have an intercept at -4
The graph of option C is the one that meets the required criteria hence the nest option
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Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x2 + 3x - 2
F(a) =
Answers
For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4
Given,
The function f(x) = x² + 3x - 2
We have to find f(a) and domain f(x - 1)
Here,
f(x) = x² + 3x - 2
Then,
f(a) = a² + 3a - 2
Now,
f(x - 1) = (x - 1)² + 3(x - 1) - 2
f(x - 1) = x² - 2x + 1 + 3x - 3 - 2
f(x - 1) = x² + x - 4
That is,
For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4
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Suppose the population of a certain city is 5700 thousand. It is expected to decrease to 4823 thousand in 50 years. Find the percent decrease.Around to the nearest tenth
Answers
We can calculate a percent change by calculating the difference between the actual state and the previous state and then dividing this difference by the previuos state.
Finally, multypling by 100% gives the percentage change.
Here we have the last state as the future population (4823 thousand people). The actual state (in this case the state to which wew want to compare the variation ir change) is 5700 thousand people.
The difference is 4823 - 5700 = -877.
Then, we can divide it by the actual population and we will have:
[tex]\frac{4823-5700}{5700}=\frac{-877}{5700}\approx0.1538[/tex]This is equivalent to:
[tex]01538\cdot100\%=15.38\%[/tex]If we have to round to nearest tenth, the percent change is 15.4%.
Find a given that the line through M(-2, a) and N(0, -2) has gradient -4
Answers
a=6
1) Given that we have M (-2, a), N(0, -2), and the gradient -4. Let's start by applying the formula for the gradient.
G = (y_2 - y_1 ) / (x_2- x_1)
2) So "a", the second coordinate of point M is equal to 6, and as the gradient is a negative number indicates a "downhill" a decreasing direction of that line.
how to calculate 1+2?
Answers
RATIOS/UNIT RATESRead and answer the question.Jessica sold 4 out of 32 boxes of the cookies her Girl Scout troop sold onSaturday. Select ALL the choices that display an equivalent ratio to thenumber of boxes Jessica sold to the total boxes sold.8 to 641:80 11O 21602:15
Answers
Which compound inequality does the number line represent
Answers
The compound ineqality which the number line represents will be 5x ≥ -15 or 5x ≤ 10 so option (B) must be correct.
What is inequality?
A difference between two values reveals whether one is greater, smaller, or fundamentally different from the other.If the sides are not equal, an expression in mathematics is said to be unequal. The result of comparing any two values is a determination of whether one is smaller, bigger, or equal to the value on the opposite side of the equation.In option (B) given that
5x ≥ -15
⇒ x ≥ -15/5
⇒ x ≥ -3
And
5x ≤ 10
⇒ x ≤ 10/5
⇒ x ≤ 2
By looking at the number line it is clear that the blue line is greater than -3 and less than 2 hence it will be correct.
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What is the equation for this? I don't understand which piece of information is irrelevant.
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It is given that she produce print of her photos at a cost of 4 dollar per print and a setup cost of 45 dollar per run.
Let the number of photos produced be x.
Then the equation formed is
[tex]C(x)=4x+45[/tex]The sellling cost given is the unnecessary data given in the question.
The total cost is determined by only the setup cost and cost produce per prints.
The graph formed for the total cost and number of photos produced is
X-axis represent the number of photos produced and Y-axis represent the total cost.
tristan asked his coworkers about how much time they spent commuting each morning Find the median
Answers
SOLUTION
In a box and whisker plot, the firt dot on the box is Q1
The second dot on the box is Q2
The third dot on the box is Q3
Q2 is the median
From what we see,
[tex]Q2=25[/tex]Hence the answer is 25, option D
6x + 14y what is the letter y in this problem?
Answers
The value of letter y in this problem is y = 6x / -14
How to solve the equationThe equation says that 6x + 14y
To solve the equation that we have here, we would have to equate to 0
such that we would have the equation as 6x + 14y = 0
6x + 14y = 0
then we would have
6x = - 14y
remember that when positives crosses over we would have it turn as negative.
Next we would have to divide through by - 14 in order to get the value of y
hence we would have
-14y / -14 = 6x / -14
then we would have y as
y = 6x / -14
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the output is 9 less than 5 times the input"
Answers
Let the output is y and the input is x, then
output is means y =
9 less than 5 times input means 9 less than 5x
Then
y = 5x - 9
write the equation of the line in slope-intercept form given the follow[tex]slope = - \frac{5}{4} \: y - intercept \: (0 \: - 8)[/tex]
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} slope=-\frac{5}{4}\: \\ y-intercept\: (0\: -8) \end{gathered}[/tex]The point-slope equation is given by:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-\frac{5}{4} \\ y-\mleft(-8\mright)=-\frac{5}{4}(x-0) \\ y+8=-\frac{5}{4}x-0 \\ y=-\frac{5}{4}x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-\frac{5}{4}x-8 \end{gathered}[/tex]The parent function y = |x| is reflected across the x-axis to obtain ________________.y = -|x|y = -|x + 1|y = |-x|y = -|x + 5|
Answers
The given function is:
[tex]y=|x|[/tex]It is reflected across the x-axis to obtain a new function. This transformation follows the rule:
[tex]g(x)=-f(x)\rightarrow reflection\text{ }across\text{ }x-axis[/tex]If we apply this rule, we obtain:
[tex]y=-|x|[/tex]The answer is y=-|x|
A group of 23 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetarium’s frequent visitor program and $13 for each student who is not a member. The total cost of the students’ tickets is $261.
Answers
Out of 23 students 19 students are the member of planetarium's frequent visitor program and 4 students are not the members.
Given,
The total number of students in a group = 23
Cost of ticket for member of planetarium's frequent visitor program = $11
Cost of ticket for the student who is not a member = $13
The total cost of the students ticket = $261
Lets take,
The number of students with membership = x
The number of students without membership = y
Total number of students, x + y = 23 -----------(1)
Now,
Total cost for the tickets, 11x + 13y = 261
Now, Multiply 13 with (1)
We get,
13x + 13y = 299
Solve for x
13x + 13y = 299 -
11x + 13y = 261
2x + 0 = 38
2x = 38
x = 38/2
x = 19
Now, put x in (1)
19 + y = 23
y = 23 - 19
y = 4
That is,
The number of students with membership is 19 and the number of students without membership is 4.
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There are 17 girls at a party with 30 guests. What fraction
of the party guests are girls?
Answers
Answer:
17/30
Step-by-step explanation:
There are 17 girls at a party with 30 guests. What fraction of the party guests are girls?
17/30
1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 2 a and b
Answers
Given
[tex]-6y^0\text{ and \lparen-6y\rparen}^0[/tex]The solutions can be seen below.
Explanation
[tex]\begin{gathered} a)\text{ }-6y^0=-6\times y^0=-6\times1=-6 \\ b)\text{ }(-6y)^0=1 \end{gathered}[/tex]In "a," only the y-value is raised to the power of 1 hence, the reason why y^0 became 1 which then multiplies -6 to get -6. However, in "b", the entire expression is raised to the power of zero, which will then give 1 as the answer.
Find the product of -0.6 and -2/5
Express your answer as a fraction or
mixed number in simplest form.
Answers
Answer:
6/25Step-by-step explanation:
1) -0.6 = -6/10
= -3/5
2) -0.6*-2/5 = (-3/5)*(-2/5)
=(-3*-2)/(5*5)
=6/25
State what additional information is required in order to know that the triangles are congruent for the
reason given.
SSS
C
D
Y
X
A) WX = ED or XY = DC
C) YW = CE
B) ZW
ZE
D) XY = DC
Answers
Answer:
C. YW≅CE
Step-by-step explanation:
SSS is used when three pairs of sides are congruent. Two pairs of congruent sides are given. YW≅CE would be the third pair and therefore prove the triangles are congruent by SSS.
Solve 2/3 (6w+12) this equation
Answers
Answer:
4w+8
Step-by-step explanation: