Answer:
A; -6
Step-by-step explanation:
Well, the cube root of 216 is just 6, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -216 is just -6
Using f(x) = 2x-3 and g(x) = 5, find f(g(3)).
7
5
3
0
None of the choices are correct.
Answer: 7
Step-by-step explanation:
[tex]g(3)=5 \implies f(g(3))=f(5)=2(5)-3=7[/tex]
If the points (2, 5), (1, 1) and (a, 3) are collinear, find the value of a.
Answer:
a = 0
(0,3)
Step-by-step explanation:
A school of salmon was swimming in the river 5 feet below the surface. To escape a hungry bear, they went down another 3 feet.
What is the position of the salmon now relative to the surface?
Using the addition operation, the position of the salmon currently relative to the surface is 8 feet below the surface.
What is the addition operation?The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.
The addition operation involves adding two or more addends to get a result known as the sum or total, using the equal symbol (=) and the addition operand (+).
The initial position of the school of salmon below the surface = 5 feet
The depth they went down further to escape the bear = 3 feet
The current position = 8 feet (5 + 3) below the surface.
Thus, based on the addition operation, the school of salmon can be located 8 feet below the surface as they attempted to escape the hungry bear.
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A region satisfies the inequalities 2 ≤ x ≤ 6 and 3 ≤ y ≤a. What value of a would give the region an area of 24 square units?
Answer: a = 9
Step-by-step explanation:
The given figure formed is a rectangle.
Area of given region (Yellow region) = 24 [tex]unit^{2}[/tex]
Length (l) = 6-2 = 4 units
Breadth (b) = a-3 units
Area = l×b
24 = 4 x (a-3)
6 = a-3
a = 9 units
In the figure, point $O$ is the center of the circle, the measure of angle $RTB$ is $28$ degrees, and the measure of angle $ROB$ is three times the measure of angle $SOT$. What is the measure of minor arc $RS$, in degrees
The measure of minor arc RS, in degrees, will be approximately 86.66
Call the intersection of BT and circle A.
And we have that angle measurement. RTB =(1/2) (a measure of minor arc RB - a measure of minor arc SA) (a measure of minor arc RB - the measure of minor arc SA)
But angle SOT equals the measure of angle SOA.
Moreover, because SOA is a central angle, its measure is the same as that of minor arc SA.
ROB has the same measure as minor arc RB since it is also a central angle.
The measure of minor arc SA= angle SOT= angle SOA=M
The measure of minor arc RB= angle ROB=4M
So we have this equation
28=(1/2)(4M-M)
56=3 M
[56/3]=M
So, minor arc S A=[tex](56 / 3)^{\circ}[/tex]
And minor arc RB =[tex]4(56/3)=(224/3)^{\circ}[/tex]
And minor arc RS =[180-(56/3)-(224/3)]=[tex](260/3)^{\circ} \approx 86.66^{\circ}[/tex]
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The complete question should be like this:
In the figure, point O is the centre of the circle, the measure of angle RTB is 28 degrees, and the measure of angle ROB is four times the measure of angle SOT. What is the measure of minor arc RS, in degrees?
The needed diagram is attached below:
Describe each correlation value.
A. r = 0.921
B. r=-0.873
C. r = -0.281
D. r = 0.303
[Select]
[Select]
[Select]
[Select]
>
>
The correlation coefficient having -negative value means inverse correlation and +positive value means direct relationship.
What Is the Correlation Coefficient?An analytical way to gauge how strongly two variables are linearly related is to use the correlation coefficient. Anywhere between -1 and 1 can be its value. A correlation coefficient of -1 indicates a perfect negative, inverse, or inverse-correlation, where values in one series increase as those in the other decline and vice versa. An exact positive correlation or direct relationship is indicated by a coefficient of 1, or 1. In the absence of a linear relationship, a correlation coefficient of 0 indicates.
When evaluating the level of association between two variables, factors, or data sets, scientists and financiers alike use correlation coefficients. Assuming, for instance, that there is a strong positive correlation between oil prices and forward returns on oil stocks given that high oil prices are advantageous for crude producers
Now,
For
A. r = 0.921 -Direct relationship.
B. r= -0.873 -Inverse relationship.
C. r = -0.281 -Inverse relationship.
D. r = 0.303 -Direct relationship.
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four horizontal lines and four vertical lines are drawn in a plane. in how many ways can four lines be chosen such that a rectangular region is enclosed?
Four lines be chosen from four horizontal lines and four vertical lines in a plane such that a rectangular region is enclosed in 36 ways.
The four horizontal lines can be chosen in 4 choose 2 = 6 ways because we have to pick 2 out of 4, and the four vertical lines can be chosen in 4 choose 2 = 6 ways as well as
4C2 = 4!/ (2!×2!)
4C2 = 6
The total number of ways to pick four lines that enclose a rectangular region is 6×6 = 36, where each combination of two horizontal lines and two vertical lines forms a rectangle.
It's important to notice that the order of choosing the lines doesn't matter, so we use the combination formula (nCr) instead of permutation formula (nPr).
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if you ate 2.5 cups of this particular cereal, how many calories and grams of fiber would you be consuming?
On solving the provided question, we can say that by linear equation we have 2.5x * cereals = y
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.
2.5 cups of this particular cereal,
the following linear equation, you could calculate how many calories and grams of fiber you were eating.
let x = cereals we eat y = calories
so, equation - 2.5x * cereals = y
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What transformation(s) have been applied to function f(x) to get g(x)? Check all that apply.translationreflectiondilationrotation
Transformations that have been applied to function f(x) to get g(x) are translation, reflection, and dilation.
The process of transforming the existing graph or graphed equation, to create a variation of the following chart is called graph conversion. Transformations such as translation, reflection, and dilation have been applied to function f(x) to produce g(x).
Whenever the function is "translated" it is moved in such a very way that it will not alter the shape or rotate in any way.The reflection is a modification of the function's graph all along the x or y-axis (or both).Dilation is defined as a stretch or shortening about in an axis caused by multiplying or subdivisions.Therefore, the answer is "translation , reflection , and dilation".
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Answer:
A) Translation
B) Reflection
C) Dilation
Step-by-step explanation:
please help me find this answer!
Answer:
[tex]k { { { {y6444396}^{46446?} }^342{?} }^66 {6 { { {6636163 \\ }^{2} }^{2} }^{2} }^{2} {?} }^{?} \times \4166441frac{?}{?} [/tex]
Step-by-step explanation:
djdkkwkwnsjididjfjrje
Coins are placed into a treasure chest, and each coin has a radius of 1.6 inches and a height of 0.0625 inches. If there are 170 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
341.63 in3
106.76 in3
85.41 in3
0.50 in3
85.41 cubic inches of the treasure chest is taken up by the coins
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Remember that the volume of a cylinder is given by:
volume = (height)×pi×(radius)²
Where pi = 3.14
Then here the volume of each coin is:
V = (0.0625)(3.14)(1.6)²
= 0.5024 in³
And there are 170 coins, so the total volume is:
170×0.5024
85.408 in³
85.41 in³
Hence, 85.41 cubic inches of the treasure chest is taken up by the coins
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Answer:
c or 85.41
Step-by-step explanation: its simple
An Isoceles right triangle whose legs measure 6 is continously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a what?
Assuming an isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object, the three-dimensional object is a: D. cone with a diameter of 12.
What are the types of triangle?In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleWhat is a right angle?In Mathematics, a right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees (90°).
Generally speaking, the resulting three-dimensional (3-D) geometric object that is formed when a right-angled triangle is continuously rotated about a leg would be a cone. Additionally, the radius of this cone would be equal to 6 because the base of the right-angled triangle is 6.
Therefore, the diameter of this cone can be calculated as follows;
Diameter of cone = 2 × radius of cone
Diameter of cone = 2 × 6
Diameter of cone = 12 units.
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Complete Question:
An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a
answer choices
cylinder with a diameter of 6
cylinder with a diameter of 12
cone with a diameter of 6
cone with a diameter of 12
Select the parallel lines from the given pairs of lines :
Select one:
a.
y = x / 3 + 11, y = x / 2 + 15
b.
y = 3x + 11, y = 3x + 15
c.
y = 3x + 11, y = − 3x + 15
d.
y = 3x + 11, y = x / 2 + 15
Answer:
b.
y = 3x + 11, y = 3x + 15
Step-by-step explanation:
Both lines have the same slope, so they are parallel.
An earthworm was in the soil 9 inches below the surface. To find moister soil, it moved down 7 inches.
What is the position of the earthworm now relative to the surface?
inches
Using the addition operation, the position of the earthworm relative to the surface is 16 inches below the surface.
What is the addition operation?One of the four basic mathematical operations, including subtraction, division, and multiplication, is the addition operation.
Using the addition operation involves adding two or more addends to determine the sum. It also involves using the addition operand (+) and the equal symbol (=).
The initial position of the earthworm below the surface = 9 inches
The depth it moved down to find moister soil = 7 inches
The current position = 16 inches (9 + 7) below the surface.
Thus, based on the addition operation, the earthworm is 16 inches below the surface in its endless search for moister soil.
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a store manager wants to mix 20 lb of nuts worth $3 per pound with some nuts worth $10 per pound to make a mixture worth $5 per pound. how many pounds of $10 nuts must be used?
a telephone company charges $0.50 for the first 5 minutes of a call and $0.09 for each additional minute. which interval below represents how a person can talk for $3 (assume that a person cannot talk for a fraction of a minute)?
On solving the provided question, we can say that by equation 15+4 = total minutes, they can talk 19 minute
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x= total minutes -4 the 1st 4 minutes are included in the .30
total cost = .3 + .18 x
[tex]3 = .3 +.18 x\\2.7 = .18x\\2.7/.18 = x\\15 = x[/tex]
x = total minutes -4
15+4 = total minutes
they can talk 19 minute
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Can anyone please help me?
Answer: C. 3
Step-by-step explanation:
Using the trapezoid midsegment theorem,
[tex]\frac{4x+8x+3}{2}=4x+7.5\\\\\frac{12x+3}{2}=4x+7.5\\\\12x+3=8x+15\\\\4x+3=15\\\\4x=12\\\\x=3[/tex]
Point Q is the center of dilation. Line W Y is dilated to created line W prime Y prime. The length of Q W is 2 and the length of W W prime is 3.5. Line WY is dilated to create line W'Y' using point Q as the center of dilation. What is the scale factor
The scale factor of the given measurement is 1.75.
The scale factor of a dilation is determined by the ratio of the length of the image to the length of the preimage. In this case, line W'Y' is the image and line WY is the preimage. We know that the length of QW is 2 and the length of WW' is 3.5.
We can use these pieces of information to calculate the scale factor. The scale factor is the ratio of the length of the image to the length of the preimage, which means it is the ratio of 3.5/2 = 1.75.
Therefore the scale factor of the dilation is 1.75.
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Multiply. x^2-1/5xy * x^2y/1+x
The required expression is x(x - 1)/5 which is determined by multiplication.
The expression is given in the question, as follows:
(x² - 1)/5xy × x²y/(1 + x)
We have to determine the solution to the given expression by multiplication.
As per the given expression, we have
⇒ (x² - 1)/5xy × x²y/(1 + x)
Cancel out the equivalent terms in the above expression,
⇒ (x - 1)(x + 1)/5 × x/(1 + x)
Reduce the same in the above expression,
⇒ x(x - 1)/5
The required expression is x(x - 1)/5.
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In 1995 the Educational Testing Service (ETS) adjusted the scores of SAT
tests. Before ETS recentered the SAT Verbal test, the mean of all test scores was 450. Which statistic would not change if 50 points were added to each score?
The statistic that would not change if 50 points were added to each score in the SAT tests is the Standard Deviation.
What happens to the standard deviation ?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance.
The bigger the deviation within the data collection, the further the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
Since they are used to determine standard deviation, sample size, mean, and data values all have an impact on standard deviation. By removing outliers, the sample size, mean, and standard deviation may all change.
Because 50 points was added to each score, they are still the same distance from each other which means the standard deviation will not change.
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describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 15 inches, 37 inches
The possible length of the third side of the triangle is x>52 inches.
What is the sum of the first side and second side of any triangle?The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. If the sum of the two sides is equal to the third side, then the two sides will coincide with the third side so a triangle cannot be formed. Hence, the sum of the two sides must be greater than the third side for the triangle to be formed.
Given: Sides of two sides of a triangle as 15 and 37 inches.
let the third side of the triangle be x.
then x>15+37
x>52 inches.
Hence, The possible length of the third side of the triangle is x>52 inches.
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A cell phone company charges 50$ for a phone plus 25$ per month. You get a gift card for 100$. When does the total spent on your phone service exceed the amount on you gift card?
A) Write an inequality to represent the money spent on a phone plan
B) when doe the total spent on your phone service exceed the amount of your gift card
Answer:
A) The money spent on a phone plan can be represented by the inequality:
50 + 25x > 100
B) The total spent on the phone service exceeds the amount of the gift card after the 2nd month.
Step-by-step explanation:
A. The inequality represents the total cost of the phone plan, where x represents the number of months for which the service is used.
The first part of the inequality, 50$, represents the initial cost of the phone.
The second part, 25x, represents the monthly cost of the service, 25$ per month.
So, the inequality represents the total cost of the phone plan as the sum of the initial cost of the phone and the monthly cost of the service for x number of months.
50 + 25x > 100
It states that the total cost (50 + 25x) of the phone plan is greater than 100$.
It's the total cost you have to pay for the phone and the service.
It's used to know when the total cost exceeds 100$, which is the gift card's value.
B. To find out when the total spent on the phone service exceeds the amount of the gift card, we can substitute in the inequality with the given values and solve for x.
50 + 25x > 100
x > (100-50)/25
x > 2
So, the total spent on the phone service exceeds the amount of the gift card after the 2nd month.
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Potatoes cost janice $1. 00 per pound, and she has $6. 00 that she could possibly spend on potatoes or other items. Suppose she feels that the first pound of potatoes is worth $1. 50, the second pound is worth $1. 14, the third pound is worth $1. 05, and all subsequent pounds are worth $0. 30 per pound.
Janice will spend $3.00 on 3 pounds of potatoes. If she only has $3.00, she will spend it all on potatoes and purchase 3 pounds of potatoes.
a) 3 pounds of potatoes
b) 3 pounds of potatoes
What is pounds?A pound is defined as 16 ounces, 7,000 grains (or 0.45359237 kg) of avoirdupois weight and 12 ounces, 5,760 grains (or 0.37324171216 kg) of troy and apothecaries' weight. The initials "lb" come from the Latin word "libra," which was the Roman equivalent of the modern "pound."
Janice can get potatoes once the price is set. As a result, she will buy those potatoes whose value is less than her willingness to pay. Her disposition to pay is what she feels the pound of potatoes is "worth". If the worth of the primary, second, and third pounds exceeds the price of the potato ($1.50, $1.14, $1.05 > $1.00), Janice will not purchase these because the worth is less than the price. (0.30 USD 1.00 USD).
Thus, Janice will spend $3.00 on 3 pounds of potatoes. If she only has $3.00, she will spend it all on potatoes and purchase 3 pounds of potatoes.
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a rectangular room is 2 times as long as it is wide, and its perimeter is 36 meters. find the dimension of the room
The dimension of the room is width = 6 meters and length = 12 meters.
What is rectangle ?
A rectangle is a four-sided polygon with opposite sides that are parallel and of equal length. It has four right angles. The two parallel sides are called the length and the width. The length is the longer of the two sides, while the width is the shorter of the two sides.
Let's assume the width of the rectangular room is "w" and the length of the rectangular room is "l"
We know that the perimeter of a rectangle is the sum of twice the length and twice the width: P = 2l + 2w
Given that the perimeter is 36 meters, we can substitute that into the equation ,
36 = 2l + 2w
We also know that the length is 2 times the width, so we can substitute that into the equation: I = 2w
Now we have two equations ,
36 = 2(2w) + 2w
36 = 6w
So the width of the room is 6 meters. To find the length, we can use the information that the length is 2 times the width ,
l = 2w = 2*6 = 12 meters
So the dimension of the room is width = 6 meters and length= 12 meters.
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A line passes through the points (–1, –5) and (4, 5). the point (a, 1) is also on the line. a coordinate plane. what is the value of a? –2 –1 1 2
The value of a is 2
We can use the slope-intercept form of a line, y = MX + b, to find the equation of the line.
The slope (m) of the line can be found using the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
So, m = (5 - (-5)) / (4 - (-1)) = 10/5 = 2
Now, we can use the point-slope form of a line, y-y1 = m(x-x1)
where (x1,y1) is any point on the line and m is the slope of the line.
In this case, we will use the point (x1, y1) = (–1, –5)
so, y-y1 = m(x-x1) = -5 - 2(-1-x) = -5-2+2x
Now we know that the point (a,1) is also on the line, we can substitute the value of x and y in the equation
so, 1 - (-5) = 2(a - (-1))
1 +5 = 2a+2
6 = 2a+2
4 = 2a
a = 2
Therefore, the value of a is 2.
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[(1/15−2/5)⋅(−3/4)³]÷(−9)
Answer:
[tex]-\frac{1}{64}[/tex]
Step-by-step explanation:
We have:
[tex][( \frac{1}{15} - \frac{2}{5}) * (-\frac{3}{4})^{3}] / (-9)[/tex]
Now, we will multiply the second fraction in the first parentheses by [tex]\frac{3}{3}[/tex] so we can subtract it from the [tex]\frac{1}{15}[/tex]. Then, we will multiply all of the [tex]\frac{3}{4}[/tex]'s. This gives us:
[tex][( \frac{1}{15} - \frac{2}{5} * \frac{3}{3} ) * (-\frac{3}{4} * -\frac{3}{4} * -\frac{3}{4})] / (-9)[/tex]
Which simplifies to:
[tex][( \frac{1}{15} - \frac{6}{15} ) * (-\frac{27}{64})] / (-9)[/tex]
Simplifying:
[tex][(-\frac{5}{15} ) * (-\frac{27}{64})] / (-9)[/tex]
Multiplying in our brackets gives us:
[tex]\frac{9}{64} / (-9)[/tex]
Now, using the rule of KCF (Keep, Change, Flip), we will keep our first fraction, change our division sign to a multiplication sign, and make the last number its reciprocal. This gives us:
[tex]\frac{9}{64} * -\frac{1}{9} = -\frac{1}{64}[/tex]
So, the equation simplified is [tex]-\frac{1}{64}[/tex].
Hope this helped!
Casey wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs %60 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?
Hi, I'm having a little bit of confusion answering this. What I did was:
Tan(20) = 9/x
9 x Tan(20) = x
But my answer was wrong, can someone tell me what I did wrong?
Thanks :)
Answer:
Step-by-step explanation:c
Select 2 points in the solution of the inequality graphed below.
654-
21
3
x
k
After its second bounce, a ball reached a height of 80 cm. The rebound factor for the ball was 0.7. From approximately what height, in cm, was the ball dropped?
A) 34
B) 49
C) 115
D) 163
Answer: The answer is C hope this helps :)
Step-by-step explanation:
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The height of a ball after its second bounce was 80 cm. The ball had a rebound factor of 0.7. Then the height of the ball from where it is dropped is given as,
0.7h = 80
h = 80 / 0.7
h = 14.3 cm
h ≈ 115 cm
The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.
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