Answer:
The answer is [tex]r=\frac{3}{2}\ cm.[/tex]
Step-by-step explanation:
Given:
V= πr²h.
V = 81 cm3,
π = 4 and
h = 9cm.
Now, making r the subject of the formula using the result from the above, find r.
So, to get the value of r:
[tex]V=\pi r^2h[/tex]
[tex]81=4\times r^2\times 9[/tex]
[tex]81=36r^2[/tex]
Dividing both sides by 36 we get:
[tex]\frac{81}{36} =r^2[/tex]
Using square root on both sides we get:
[tex]\frac{9}{6} =r[/tex]
[tex]\frac{3}{2} =r[/tex]
[tex]r=\frac{3}{2}.[/tex]
Therefore, the answer is [tex]r=\frac{3}{2}\ cm.[/tex]
If the sum of a number and five is doubled, the results is one less than the number.find the number
The number that satisfies the condition that, when added to five and then doubled, is one less than the number itself is -11. We found this number by setting up an equation and solving for the variable.
Explanation:Let's define x to be the number we're trying to find. According to the question, if the sum of this number and five is doubled, the result is one less than the number.
The equation based on the given information is 2(x + 5) = x - 1. To solve for x, let's distribute the 2 to both terms in the parentheses: 2x + 10 = x - 1.
Next, we need to get all the x terms on one side and the constant terms on the other side. We can do this by subtracting x from both sides, giving us: x + 10 = -1. Then, subtract 10 from both sides to isolate x: x = -11. So, the number we're looking for is -11.
Consider a simple economy where the basket of goods used to calculate the CPI contains two items: shirts and pants. The basket consists of 3 shirts and 2 pairs of pants. Each item increases in price by $1 in year 2. The pants price is 20$ and the shirt price is 25$. What is the CPI for year 2.
To calculate the CPI for year 2 in a simple economy involving shirts and pants, we first find the total cost of the basket in both years considering the price increase. Then, using the formula for CPI, we find that the CPI for year 2 is 122.45, indicating an increase in the average price level compared to the base year.
Explanation:To calculate the Consumer Price Index (CPI) for year 2 in a simple economy with only shirts and pants in the basket of goods, we first need to understand the concept of CPI. The CPI represents the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services. Here, we're given that the price of each item increases by $1 in year 2, with the new prices being $21 for pants and $26 for shirts.
First, calculate the total cost of the basket in year 2:
Cost of 3 shirts in year 2 = 3 shirts * $26 per shirt = $78
Cost of 2 pairs of pants in year 2 = 2 pants * $21 per pants = $42
Total cost of the basket in year 2 = $78 + $42 = $120
To determine the CPI for year 2, we also need to know the base year's total cost, which isn't directly provided here.
However, assuming the base year (year 1) prices were $1 less for each item, the prices would have been $20 for shirts and $19 for pants.
Cost of the basket in year 1:
Cost of 3 shirts = 3 shirts * $20 per shirt = $60
Cost of 2 pairs of pants = 2 pants * $19 per pants = $38
Total cost of the basket in year 1 = $60 + $38 = $98
Finally, to calculate the CPI for year 2, we use the formula:
CPI for year 2 = (Total cost of the basket in year 2 / Total cost of the basket in year 1) * 100
= ($120 / $98) * 100 = 122.45
Therefore, the CPI for year 2 is 122.45, indicating prices have increased on average when comparing year 2 to the base year (year 1). This helps in understanding the inflation rate and cost of living increases for consumers.
I costs $36 for 4 movie tickets, What is
Ovie tickets, What is the unit price of each ticket
I
Answer: $9 per ticket
Step-by-step explanation: Unit price means the cost per unit. In this case, the cost per ticket.
Since we know that it costs $36 for 4 movie tickets, to find the cost for 1 movie ticket, we need to divide 4 into $36 or 4 into 36.
4 divides into 36 9 times. 9 x 4 is 36 and 36 - 36 is 0. So 4 divides into 36 9 times which means that each movie ticket costs $9.
So the unit price is $9 per ticket.
What is the right-hand limit of this function at x = 2?
g(x) =x^2-3/x-3
Answer:
-1
Step-by-step explanation:
A function assigns the values. The right-hand limit of this function at x=2 is -1.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The right-hand limit of the function when the value of x=2, can be found by substituting the value of x as 2 in the given function, therefore, the right-hand limit of this function at x=2 is,
g(x) = (x²-3)/(x-3)
g(2) = (4-3)/(2-3)
g(2) = -1
Hence, the right-hand limit of this function at x=2 is -1.
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Ryan and his children went into a bakery and will buy cupcakes and donuts.
Each cupcake costs $4.50 and each donut costs $1.75. Ryan has a total of $40
to spend on cupcakes and donuts. Write an inequality that would represent
the possible values for the number of cupcakes purchased, c, and the number
of donuts purchased, d.
The inequality which represents the possible values for the number of cupcakes and donuts is : 4.50c + 1.75d = 450
Let :
cupcakes = cdonut = d Total amount spent = 450Expressing the scenario as an inequality :
4.50c + 1.75d = 450
Therefore, the inequality which represents the possible values for the number of cupcakes and donuts is : 4.50c + 1.75d = 450
a point is reflected in the x-axis the new point is (5, -3.5) what is the distance between the two points? Urgent pls help
Distance between two points is 7
Explanation:
This is a question based on reflection of point w.r.t line. During reflection we can see the mirror image with t-shirt print inverted.But the distance from mirror remains same.
Assume a point (x,y), and it reflect in x-axis, then x-axis serves as the mirror, and the new point is (x,-y), because the distance from the mirror remains same. If the reflection of the point is (x,y) in y-axis, then y-axis serves as the mirror, and the new point is (-x,y). And if you reflect (x,y) in y=x line, then new point will be (y,x).
So considering the above question, if new point is (5, -3.5), then the original point must be (5, 3.5)
Distance between two points [tex]P(X_1, Y_1)[/tex] and [tex]Q(X_2, Y_2)[/tex]is given by:
d(P, Q) = [tex]\sqrt{ (X_2-X_1)^{2} + (Y_2-Y_1)^{2}}[/tex]
[tex]Y_2-Y_2 = (3.5) - (-3.5) = 3.5+3.5 = 7\\ \\X_2-X_1 = 5 - 5 = 0[/tex]
[tex]So \sqrt {(Y_2-Y_1)^{2} + (X_2-X_1)^{2}} = \sqrt { 7^{2} + 0^{2}} = \sqrt { 14+0} = \sqrt {14} = 7[/tex]
So distance = 7
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4. Suppose the point B(2,8) is reflected across the x-axis and then translated according to the rule (x,y)→(y,x+4). What are the coordinates of B''? Show your work and explain.
Step-by-step explanation:
Point B(2, 8) reflect to x-axis
It means the x value won't change, the only thing that will change is the y value.
According to it, we can know that B' is (2, -8)
(2, -8) → (-8, 2+4) = (-8, 6) = B''
Final answer:
To obtain the coordinates of B'' after a reflection across the x-axis and a translation of (x,y)
ightarrow(y,x+4), point B(2,8) becomes B'(2,-8) after reflection and then B''(-8, 6) after translation.
Explanation:
The student is asking about the results of performing a geometric transformation on a point in the coordinate plane. Specifically, point B(2,8) is first reflected across the x-axis, and then is translated according to the rule (x,y)
ightarrow(y,x+4). To find the coordinates of B'', we follow these steps:
Reflect B across the x-axis: The x-coordinate remains the same, but the y-coordinate changes sign, resulting in B'(2,-8).
Apply the translation rule: We then take the coordinates of B' and apply the rule. The x-value of B' becomes the y-value of B'' and the y-value of B', decreased by 4, becomes the new x-value. Therefore, B'' = (-8, 2+4) = (-8, 6).
The final coordinates of B'' after the reflection and translation are (-8,6).
n a simple random sample of 219 students at a college, 73 reported that they have at least $1000 of credit card debt.
Which interval is the 99% confidence interval for the percent of all the students at that college who have at least $1000 in credit card debt?
(31.0 ,35.6)
( 30.1 , 36.5)
(25.0 ,41.6)
(27.5 ,39.1 )
Answer:
[tex]0.333 - 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.251[/tex]
[tex]0.333 + 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.416[/tex]
The 99% confidence interval would be given (0.251;0.416).
(25.0 ,41.6)
Step-by-step explanation:
1) Data given and notation
n=219 represent the random sample taken
X=73 represent the students that reported that they have at least $1000 of credit card debt.
[tex]\hat p=\frac{73}{219}=0.333[/tex] estimated proportion of students that reported that they have at least $1000 of credit card debt.
[tex]\alpha=0.01[/tex] represent the significance level
z would represent the statistic (variable of interest)
p= population proportion of students that reported that they have at least $1000 of credit card debt.
2) Confidence interval
The confidence interval would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 99% confidence interval the value of [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2=0.005[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=2.58[/tex]
And replacing into the confidence interval formula we got:
[tex]0.333 - 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.251[/tex]
[tex]0.333 + 2.58 \sqrt{\frac{0.333(1-0.333)}{219}}=0.416[/tex]
And the 99% confidence interval would be given (0.251;0.416).
We are confident that about 25.1% to 41.6% of students have at least $1000 of credit card debt.
And for this case the most accurate option is:
(25.0 ,41.6)
HELP ASAP NEED THIS.
Answer:
B
Step-by-step explanation:
The 2 part of the ratio represents 39 instructors.
Dividing 39 by 2 gives the value of one part of the ratio, that is
39 ÷ 2 = 19.5 ← value of 1 part of the ratio, thus
number of employees = 12 × 19.5 = 234 → B
(8,4); m=7 what’s the answer in point-slope form
The equation of line in point slope form is y - 4 = 7x - 56
Solution:
Given that m = 7 and point is (8, 4)
We have to find the equation of line in point slope form
It emphasizes the slope of the line and a point on the line
The point slope form is given as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where "m" is the slope of line
Substitute m = 7 and (x, y) = (8, 4) in above point slope form
[tex]y - 4 = 7(x - 8)[/tex]
[tex]y - 4 = 7x - 56[/tex]
Thus equation of line in point slope form is found
We can write the equation in standard form
The standard form of an equation is Ax + By = C. In this kind of equation, x and y are variables and A, B, and C are integers.
[tex]y - 4 = 7x - 56\\\\7x - y -52 = 0[/tex]
Audrey has 400 songs on her MP3 player. Of these songs, 150 are by female vocalists, 75 are by male vocalists, and 175 are by groups. If one song is played at random, what is the probability it is sung by a female vocalist?
Probability for male = 75/400 = 3/16
Probability for groups = 175/400 = 7/16
Probability for female = 150/400 = 3/8
There is a 3/8 probability of the song being sung by a female vocalist.
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Amber rides m miles in h hours according to the equation m=2h. Which of the following represents the unit rate for her miles per hour?
Answer:
The unit rate for her riding in miles per hour is given by 2 miles per hour.
Step-by-step explanation:
Amber rides m miles in h hours according to the equation m=2h .......... (1)
Putting h = 1 hour, we get m = 2 miles.
Therefore, Amber rides 2 miles height within a period of time 1 hour.
Therefore, the unit rate for her riding in miles per hour is given by 2 miles per hour. (Answer)
Again, differentiating equation (1) with respect to h we get,
[tex]\frac{dm}{dh} = 2[/tex] miles per hour.
So, here also we get the unit rate of her riding is 2 miles/hr.
5.) Juan answered 24/25 correctly on his quiz.
What percent of the questions did he get correct?
Answer:
96%
Step-by-step explanation:
Answer:
Step-by-step explanation:
Percentage = (24/25) * 100 = 24* 4 = 96%
write as a fraction and simplify 4^-4
Answer:
1/256
Step-by-step explanation:
1/256
4^-4 as a fraction is 1/256. It cannot be further simplified because 1 and 256 have no common factors other than 1, making it the simplest form.
To express 4^-4 as a fraction and simplify it, we can apply the rule that states any non-zero number raised to a negative exponent is equivalent to 1 divided by that number raised to the positive exponent.
So, for 4^-4, we can write it as:
4^-4 = 1 / 4^4
Now, let's calculate 4^4:
4^4 = 4 * 4 * 4 * 4 = 256
So, we have:
4^-4 = 1 / 256
This is the fraction representation of 4^-4. To determine if it can be further simplified, we can check if the numerator and denominator have any common factors other than 1. In this case, 1 and 256 have no common factors other than 1.
Therefore, 1/256 is already in its simplest form. It represents the fraction equivalent of 4^-4, which is a small value. It means that 4 raised to the power of -4 is a very small positive number, specifically 1/256, indicating that the original number 4^-4 is less than 1 and quite close to zero in value.
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Find the value of the greater root of x2 - 6x + 5 = 0.
A) -5
B) -1
C) 1
D) 5
Answer:
D
Step-by-step explanation:
We need to find 2 roots of the quadratic function given and find the greater of the two roots.
We factorize the quadratic and find the two solutions first:
[tex]x^2-6x+5=0\\(x-5)(x-1)=0\\x=1,5[/tex]
So,
x = 1
and
x= 5
Out of the two, x = 5 is the greater root.
D is the correct answer.
$7 is what percent of 10$
Answer:
7/10
Step-by-step explanation:
you got 7 out of 10 dollars
Answer:
70%
Step-by-step explanation:
Because the fraction would be 7/10 when you make it to precent form it would be 70/100 which is 70%
Solve 2 cos ø + 2=3 in the interval from 0 to 2 π.Round to the nearest hundredth.
Answer:
The value of ∅ for the given trigonometrical equation is 60° .
Step-by-step explanation:
Given as :
The Trigonometrical equation
2 cos∅ + 2 = 3
Now, Solving this equation to get the value of ∅
∴ The equation can be written as
2 cos∅ = 3 - 2
or , 2 cos∅ = 1
or , cos∅ = [tex]\dfrac{1}{2}[/tex]
∴ ∅ = [tex]cos^{-1}(\frac{1}{2})[/tex]
I.e ∅ = 60°
So,The value of ∅ for the given trigonometrical equation = ∅ = 60°
Hence, The value of ∅ for the given trigonometrical equation is 60° . Answer
Mrs. Jacobs is making several batches of cookies and is using 84 total ounces of chips. The cookies have chocolate chips and peanut butter chips. There are 5 times as many ounces of chocolate chips as peanut butter chips. How many ounces of chocolate chips does Mrs. Jacobs use?
The ounces of chocolate chips used by Mrs Jacob is 70 ounce
Solution:
Given that Jacob is making several batches of cookies and is using 84 total ounces of chips
Let "c" be the ounces of chocolate chips
Let "p" be the ounces of peanut butter chips
To find: ounces of chocolate chips used by Mrs Jacob
Given that There are 5 times as many ounces of chocolate chips as peanut butter chips
Thus we can frame a equation as:
ounces of chocolate chips = 5 x ounces of peanut butter chips
c = 5p -------- eqn 1
Jacob used 84 total ounces of chip. Therefore,
ounces of chocolate chips + ounces of peanut butter chips = 84
c + p = 84 ---- eqn 2
Substitute eqn 1 in eqn 2
5p + p = 84
6p = 84
p = 14Substitute p = 14 in eqn 1
c = 5(14) = 70
c = 70Thus the ounces of chocolate chips used by Mrs Jacob is 70 ounce
g(x) = 2x + 9
g( )= 15
If g(x)=15, x=...
g(x)=15
2x+9=15
x=3
answer: 3
Answer:
the answer is 3
Step-by-step explanation:
Jerome's average speed for walking is 13 minutes and 40 seconds per mile. He will be walking for a fundraiser a total of 12 miles. Based on his average speed, how long should it take him to finish?
Answer:
164 minutes
Step-by-step explanation:
Assuming that Jerome's seed is maintained, we say that for every 1 mile, he takes 13 minutes and 40 seconds which is equivalent to[tex]13\frac {2}{3}[/tex] since 1 minute has 60 seconds hence [tex]\frac {40}{60}[/tex]=[tex]\frac {2}{3}[/tex]
Now if
1 mile = [tex]13\frac {2}{3}[/tex]
12 miles=??
We cross multiply hence 12\times[tex]13\frac {2}{3}=164[/tex]
Therefore, Jerome needs 164 minutes, equivalent to 2 hours 44 minutes
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The segment to draw is segment UT
Step-by-step explanation:
A line segment is a part of a line that is bounded by two two distinct end points. In this case, segment UT is bounded by endpoints U and T. In the diagram, point R is not a segment but a point of intersection of segments BT and EU.
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O
These are the means and standard deviations for samples of heights from
two kinds of trees.
Tree A
Mean: 25 ft
Standard deviation: 5 ft
Tree B
Mean: 60 ft
Standard deviation: 12 ft
rol
O
.
Select the two true statements.
Oh
CTS
(
DC)
I
A. Tree A's heights are less spread out than tree B's heights.
O
B. Tree A has a lower average height than tree B.
O
C. Tree A's heights are more spread out than tree B's heights.
D Tree A has a greater average height than tree B
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The true statements are:
A. Tree A's heights are less spread out than tree B's heights and
B. Tree A has lower average height than tree B
Explanation:
Standard deviation in this case represents the spreading out of heights of the trees, Since tree A has lesser standard deviation given equal to 5 , it is less spread out than B given equal to 12, hence option A. is true.
The average of a quantity is given by mean so, the average height can be compared by the given mean values of the trees. Since, A has lesser mean value (= 25) than B(=60), tree A is said to have lower average height than tree B hence option B. is true.
Answer:
A and B
ITS RIGHT FOR ME!!!!!!!The pyramid shown has a square base that is 24
24
centimeters on each side. The slant height is 16
16
centimeters. What is the lateral surface area?
Answer:
[tex]768\ cm^{2}[/tex]
Step-by-step explanation:
Here is the correct question: The pyramid shown has a square base that is 24 centimeters on each side. The slant height is 16 centimeters. What is the lateral surface area?
Given: Side of sqaure base = 24 cm
Slant height= 16 cm
Now, we have to compute to know lateral surface area of Pyramid with square base.
Formula, lateral surface area of pyramid= [tex]4(\frac{1}{2} \times b\times h)[/tex]
we know, side of sqaure base (b) is 24 cm and slant height (h) is 16 cm.
lateral surface area of pyramid= [tex]4\times (\frac{1}{2} \times 24\times 16)[/tex]
⇒lateral surface area of pyramid= [tex]4\times (192)[/tex]
Opening parenthesis.
∴lateral surface area of pyramid= [tex]768\ cm^{2}[/tex]
Find the slope of the line that passes through (9,9) and(2,1)
Answer:
8/7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-9)/(2-9)
m=-8/-7
m=8/7
Answer:
m= 8/7
Step-by-step explanation:
the formula to find slope is
m= y2-y1/x2-x1
(I WILL GIVE BRAINLIEST)
what are the apparent zeroes of the function graphed above?
A. {-1, 2.5}
B. {-17, 5}
C. {-4, 0, 2}
D. {-2, 0 , 4}
Answer:
So the correct option is D
{-2 , 0 , 4}
Step-by-step explanation:
Given:
A Graph
To Find:
Zeroes of the function graph = ?
Solution:
Zeroes of Graph:
Wherever the function graphs line cuts the x-axis are called ZEROES of the function graphs.
Here there are three different points were the function graphs cuts on x-axis. Therefore three zeroes,which are -2 , 0 , 4
i.e x = - 2 , x = 0 (origin),and x = 4
So the correct option is D
{-2 , 0 , 4}
Define a translation and explain why it is a congruent figure
Express sin6θ + sin4θ as a product.
Answer: [tex]2 sin(5 \theta) cos \theta[/tex]
Step-by-step explanation:
According to the trigonometric identities we have the following formula:
[tex]sin (x) + sin (y)=2 sin(\frac{x+y}{2}) cos(\frac{x-y}{2})[/tex]
Now, we have the following:
[tex]sin (6\theta)+ sin (4\theta)[/tex]
Where [tex]x=6\theta[/tex] and [tex]y=4\theta[/tex]
Hence:
[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{6\theta+4\theta}{2}) cos(\frac{6\theta-4\theta}{2})[/tex]
[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{10\theta}{2}) cos(\frac{2\theta}{2})[/tex]
Finally:
[tex]sin (6\theta)+ sin (4\theta)=2 sin(5\theta) cos(\theta)[/tex]
Solve:
2(−n−3)−7(5+2n)
Answer:
-16n-41
Step-by-step explanation:
2(-n-3)-7(5+2n)
First begin by expanding the bracket. That is, multiplyingthe brackets by 2 and -7 appropriately.
In doing so we have,
2(-n) x 2(-3) -7(5) x -7 (+2n)
simplifying becomes:
-2n-6-35-14n
collwct like terms becomes -2n-14n-6-35
Final answer becomes Thus: -16n-41
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X= ____________
Answer:
x = 26
Step-by-step explanation:
The parallel lines are Line l and Line m. The other line shown is the transversal.
When 2 parallel lines are cut by a trasversal it creates 4 euqual angles and another 4 equal angles of different measure.
The angle "5x + 7" is equal to the angle "8x - 71" since they are alternate exterior angles.
So, we can equate both expressions and use algebra to solve for "x". The process is shown below:
[tex]5x+7=8x-71\\8x-5x=71+7\\3x=78\\x=\frac{78}{3}\\x=26[/tex]
Hence,
the value of x is 26
Can someone help me please
Answer:
both are answered below
Step-by-step explanation:
let us assume that , he buys y number of roses and x carnations.the total cost cant be more than $30.the cost of each rose : $3the cost of each carnation : $2so, the cost of all roses that he buys : 3xthe cost of all carnations that he buys : 2ythe required inequality will be : 3x+2y[tex]\leq[/tex]30the graph is in the attachment.by seeing graph, possible x,y values: (2,12) , (6,6) , (8,3)[where x represents no. of carnations that he buys , y represents no. of roses that he buys ]