Using the Pythagorean theorem:
Length of wire = sqrt(34^2 + 8^2)
Length of wire = sqrt(1156 +64)
Length of wire = sqrt(1220)
Length of wire = 34.9285 feet
There are 2 wires:
34.9285 x 2 = 69.857 feet
Round off as needed.
Answer:
34.93 feet
Step-by-step explanation:
Using a^2+b^2=c^2
we can substitute a and b in which is
34^2+8^2=c^2
1156+64=c^2
1220 = c^2
Now we need to square both sides
√1220 = √c^2
34.9284983931 ----> 34.93
34.93 = c
c = 34.93
Lai Lal Chinese Restaurant has seven items in its breakfast menu. The management of Lai Lai has just acquired some data and they would like to find out both popularity and profitability of its breakfast menu items based on their selling price, food cost percentage, sales volume and contribution margin (CM) from the past period. The financial data for the selling price, sales volume, and individual food cost dollar amounts are presented in the table below:
Breakfast Selling Price Food Cost Menu Item ($) (52 Sales Volume А $10.00 $3.00 250 B $16.00 $6.00 50 с $18.45 $8.00 60 D $14.75 $4.25 300 E $8.75 $2.50 80 F $12.50 $5.75 180 G $9.00 $2.60 280 TOTAL 1.200
Based on the information given in the table above, what are the specific classification of the breakfast menu items based on their profitability and popularity in order?
Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.
What is the contribution margin?The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.
The contribution margin can be computed per unit or in total. Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.
Breakfast Selling Price Food Cost Sales Contribution Margin
Menu Item ($) ($) Volume Unit Total
А $10.00 $3.00 250 $7.00 $1,750
B $16.00 $6.00 50 $10.00 $500
C $18.45 $8.00 60 $10.45 $627
D $14.75 $4.25 300 $10.50 $3,150
E $8.75 $2.50 80 $6.25 $500
F $12.50 $5.75 180 $6.75 $1,215
G $9.00 $2.60 280 $6.40 $1,792
TOTAL 1,200
Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.
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Select the correct answer.
Which statement best defines a circle?
OA the set of all points in a plane that are the same distance from a given point called the center
OB. the set of all points that are the same distance from a given point called the center
OC points in a plane that surround a given point called the center
OD. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
Reset
Next
Answer:
A. the set of all points in a plane that are the same distance from a given point called the center
Step-by-step explanation:
A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally
distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what percentage of cars
are driving less than 65 mi/hr? Use the empirical rule to solve the problem. (Round to the nearest tenth of a
percent)
The solution is : the percentage of cars that are driving less than 45 mi/hr is 2.3%
Here, we have,
Since the speeds of cars are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = speeds of cars
µ = mean speed
σ = standard deviation
From the information given,
µ = 55 mi/hr
σ = 5 mi/hr
The probability that a car is driving less than 45 mi/hr is expressed as
P(x < 45)
For x = 45
z = (45 - 55)/5 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
Therefore, the percentage of cars that are driving less than 45 mi/hr is
0.023 × 100 = 2.3%
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1.1.4 Express 25/75 as a percentage.
Answer:
Hi
Please mark brainliest ❣️
Step-by-step explanation:
25/75 × 100/1
= 33.3%
10.
A lunch menu consists of 8 different sandwiches, 5 different soups, and 3 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?
65 choices
120 choices
165 choices
16 choices
For the given menu, there are 120 choices for ordering a sandwich, a bowl of soup, and a drink.
Using the Multiplication PrincipleNumber of choices for ordering:
Sandwich = 8
Soup = 5
Drink = 3
According to the multiplication principle, multiply the number of options for each category to find the total number of choices:
Total choices = (Number of options for Sandwich) * (Number of options for Soup) * (Number of options for Drink)
Total choices = 8 * 5 * 3
Total choices = 120
Therefore, there are 120 choices for ordering a sandwich, a bowl of soup, and a drink from the given menu.
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PLEASE I NEED HELP !!!!!
The weight of a pitaya seed in standard form is [tex]1 \times 10^-^6[/tex]ounce.
In standard form, the weight of a pitaya seed is expressed in scientific notation, where the number is a decimal between 1 and 10, and the exponent is a power of 10. The weight of a pitaya seed is given as [tex]1 x 10^-^3[/tex] ounce, which means that the seed weighs one-thousandth of an ounce.
To write this in standard form, we first convert the number to a decimal between 1 and 10 by moving the decimal point three places to the left. This gives us a decimal of 0.001. The exponent is already in the form of a power of 10, so we can leave it as [tex]10^-^3[/tex]. Thus, the weight of a pitaya seed in standard form is:
[tex]0.001 \times 10^-^3[/tex]
To simplify this expression, we can multiply the decimal and the exponent. This gives us:
[tex]1 x 10^-^6[/tex]
This means that the weight of a single pitaya seed is very small, and it takes many seeds to make up the weight of a whole pitaya fruit.
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HELPPPPPPPP!!!!!!!!!!!!! Answer this please
The surface area of the cuboid that has length = 4 yd, width = 2 yd and height = 3 yd is 44 square yards.
To find the surface area of a cuboid, we need to add up the area of all six faces. The formula for the surface area of a cuboid is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the cuboid, respectively.
Substituting the given values, we get:
Surface Area = 2(4 x 2) + 2(4 x 3) + 2(2 x 3)
Surface Area = 8 + 24 + 12
Surface Area = 44
This means that there are 44 square yards of material needed to cover all six faces of the cuboid.
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The figure below shows a triangle with vertices, a and B on a circle and vertex c outside it. Side ac is tangent to the circle. Side bc is a secant intersecting the circle at point x. What is the measure of angle acb?
1.32
2.60
3.28
4.16
The measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.
The measure of angle ACB can be determined using the properties of tangents and secants intersecting a circle.
Since side AC is tangent to the circle, angle BAC is a right angle (90 degrees).
According to the tangent-secant theorem, the measure of angle ACB is equal to half the difference between the intercepted arcs AB and AX.
Since angle BAC is a right angle, the intercepted arc AX is a semicircle, which means its measure is 180 degrees. The intercepted arc AB is an arc of the circle and is less than 180 degrees since it is not a full circle.
Therefore, the measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.
To find the exact measure, more information is needed about the length of arc AB or the relationship between the lengths of the sides of the triangle. Without this additional information, we cannot determine the precise measure of angle ACB.
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A rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm² What is the side length of its base?
If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.
Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².
We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:
x² * 17.2 cm³ = 24.768 cm³
Simplifying this equation, we get:
x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²
Taking the square root of both sides, we get:
x = 1.2 cm
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1
4
(
8
−
6
x
+
12
)
?
1
4
(
8
−
6
x
+
12
)
?
A.
7
2
x
7
2
x
B.
−
13
2
x
−
13
2
x
C.
−
6
x
+
14
−
6
x
+
14
D.
−
3
2
x
+
5
The equivalent expression is 5 - 3x/2. Option D
What are algebraic expressions?Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.
these algebraic expressions are also composed of mathematical operations. These operations includes;
BracketParenthesesSubtractionMultiplicationDivisionAdditionFrom the information given, we have that;
1/ 4(8 - 6x + 12)
expand the bracket, we have;
Add the like terms
1/4(20 - 6x)
now, multiply the values, we have;
20 - 6x/4
Divide by the denominator
5 - 3x/2
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The complete question:
Simply the expression:
1/ 4(8 - 6x + 12)
Thirty-four percent of workers in the Unites States are college graduates. Suppose a random sample of 120 workers is obtained and 35 of them have a college degree.
a) What are the mean and standard deviation of the number of workers with a college degree respectively?
b) What is the probability that the number of workers with a college degree is at least 35?
The mean number of workers with a college degree is 40.8, and the standard deviation is 5.37.
The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.
Given Sample size (n) is 120 workers
Proportion of workers who are college graduates (p): 34% or 0.34
a) Mean and Standard Deviation:
The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ =√np(1 - p).
Substituting the values:
μ = 120 ×0.34 = 40.8
σ = √120 × 0.34 × (1 - 0.34)) = 5.37
To find the probability that the number of workers with a college degree is at least 35
we need to calculate the cumulative probability of the binomial distribution from 35 to the maximum possible value, which is 120 in this case.
Using a binomial probability calculator or a statistical software, we can find this probability.
Assuming a binomial distribution with parameters n = 120 and p = 0.34, the probability can be calculated as follows:
P(X ≥ 35) = 1 - P(X < 35)
The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.
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a moving streaming service offers two types of subscriptions
A moving streaming service offers two types of subscriptions: a basic subscription and a premium subscription.
The moving streaming service provides customers with two distinct types of subscriptions to cater to their viewing preferences and needs. The first option is the basic subscription, which offers access to a limited selection of movies and TV shows. This subscription provides users with a basic streaming experience, allowing them to enjoy a range of popular titles at a lower cost.
On the other hand, the second option is the premium subscription, which provides subscribers with a more extensive and premium streaming experience. With the premium subscription, users gain access to a wider library of content, including exclusive movies, TV series, and original productions. Additionally, premium subscribers often enjoy additional features such as ad-free streaming, simultaneous streaming on multiple devices, and the ability to download content for offline viewing.
By offering these two subscription options, the moving streaming service aims to cater to a diverse range of users, providing them with flexibility and choice based on their preferences and budget.
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Find all Solutions of the equation
Answer:
[tex]\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}[/tex]
Step-by-step explanation:
To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:
[tex]\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}[/tex]
Set each factor equal to zero and solve for x using the unit circle.
[tex]\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}[/tex]
[tex]\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}[/tex]
Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:
[tex]\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}[/tex]
A 50 foot rope is stretched tight from the roof of a building to a spot 20 feet from the base of the
building. How tall is the building? Round your answer to TWO decimal places.
47.17 feet is the height of the building.
We can use the Pythagorean theorem to solve the problem:
Let h be the height of the building.
Then we have a right triangle with legs 20 and h, and a hypotenuse 50.
Using the Pythagorean theorem, we have:
[tex]50^2 = 20^2 + h^2[/tex]
Simplifying and solving for h, we get:
[tex]h = \sqrt{(50^2 - 20^2)[/tex]
h ≈ 47.17 feet (rounded to two decimal places)
Therefore, the height of the building is approximately 47.17 feet.
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6
Select ALL the true statements about 388.33.
The value of the tens digit, 80, is 10 times the value of the ones digit, 8.
The value of the hundredths digit, 0.03, is 10 times the value of the tenths
digit, 0.3.
C. The value of the ones digit, 8, is the value of the tens digit, 80.
D.
The value of the hundredths digit, 0.03, is to the value of the tenths
digit, 0.3.
A.
B.
E. O The value of the tenths digit, 0.3, is 10 times the value of the hundredths
digit, 0.03.
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
We have,
The statement "The value of the tens digit, 80, is 10 times the value of the one's digit, 8" is incorrect. The tens digit is actually 3, not 80.
The statement "The value of the hundredths digit, 0.03, is 10 times the value of the tenths digit, 0.3" is true.
The hundredth digit is 3 times smaller than the tenth digit, which means that the tenth digit is 10 times larger than the hundredth digit.
The statement "The value of the one's digit, 8, is the value of the tens digit, 80" is incorrect.
The tens digit is 3, not 80.
The statement "The value of the hundredths digit, 0.03, is to the value of the tenths digit, 0.3" is unclear and not a proper comparison, so it cannot be determined whether it is true or false.
Thus,
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
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Simplify (2x + 3)(x − 4) = ? A. 2x² - 5x + 12 O B. 2x²5x - 12 O C. 2x² + 5x + 12 O D. 2x² + 5x - 12
Answer:
2x^2-5x-12
Step-by-step explanation:
(2x+3)(x-4) can be simplified using the acronym FOIL, which stands for "first, outer, inner, last." This means that you multiply the first terms in each group, the the outer terms, then the inner terms, and lastly the last terms in each group.
2x*x=2x^2
2x*-4=-8x
3*x=3x
3*-4=-12
Combine those and you get 2x^2-8x+3x-12. Combine like terms, and your final answer is 2x^2-5x-12
please helppp!!! thank you!
The number line that shows the solution to the inequality is given as follows:
First number line.
How to solve the inequality?The inequality in the context of this problem is defined as follows:
-6x + 5 >= 17
-6x >= 12.
Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:
6x <= -12.
Then the solution is given as follows:
x <= -2.
Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.
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The number line that shows the solution to the inequality is: C. graph C.
What is an inequality?In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Based on the information provided above, we have the following equation (inequality);
-6x + 5 ≥ 17
By subtracting 5 from both sides of the equation (inequality), we have;
-6x + 5 - 5 ≥ 17 - 5
-6x ≥ 12
x ≤ 12/6
x ≤ 2 (it would be shaded to the left with a closed circle at 2).
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You pay for a fiction book, a nonfiction book, and a bookmark with three $5 bills. The fiction book costs $5.43. The nonfiction book costs $3.89. Your change is $3.45. How much does the bookmark cost?
Answer:
2.23
Step-by-step explanation:
You have 3 $5 bills which us 15 dollars. 15 dollars - 5.43 - 3.89 - 3.45 = 2.23 dollars for the bookmark.
To see if you are correct, you can add 3.45, 2.23, 3.89, and 5.43 to get your answer.
Solve the following system of equations using the elimination method
y + 2x = 1
3x - 2y = 5
The solution to the system of equations is x = 1,y = -1 by using the elimination method.
To solve the system of equations using the elimination method, we'll eliminate one variable by adding or subtracting the equations. Here's how:
Multiply the first equation by 2 to make the coefficients of y in both equations opposite each other:
Equation 1: 2(y + 2x) = 2(1) => 2y + 4x = 2
Rewrite the second equation as:
Equation 2: 3x - 2y = 5
Now, we can add the modified Equation 1 to Equation 2 to eliminate y:
(2y + 4x) + (3x - 2y) = 2 + 5
Simplifying, we get:
4x + 3x = 7
7x = 7
Divide both sides of the equation by 7 to solve for x:
x = 7/7
x = 1
Substitute the value of x into either of the original equations. Let's use the first equation:
y + 2(1) = 1
y + 2 = 1
Subtract two from both sides of the equation to solve for y:
y = 1 - 2
y = -1
Therefore, the solution to the system of equations is:
x = 1
y = -1
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Haleigh decides that instead of throwing away old candles, she can use the last bit of wax combined together to make new candles. Each candle has 10% of it's original wax left. How many 5 ounce candles can she make if she has five 20 oz candles, 5 five ounce candles, and twenty-five one-ounce candles?
We cannot have a fractional number of candles, Haleigh can make a maximum of 2 five-ounce candles using the available wax from the 20-ounce and 1-ounce candles.
To determine the number of 5-ounce candles Haleigh can make using the remaining wax from her existing candles, we need to calculate the total amount of wax available and divide it by the amount of wax needed for each 5-ounce candle.
Let's calculate the total amount of wax available:
The five 20-ounce candles have 10% of their original wax remaining, so each candle has 2 ounces of wax left.
Therefore, the total wax from the five 20-ounce candles is 5 candles [tex]\times[/tex] 2 ounces = 10 ounces.
The five 5-ounce candles already have wax, so we don't need to consider them.
The twenty-five 1-ounce candles have 10% of their original wax remaining, so each candle has 0.1 ounces of wax left.
Therefore, the total wax from the twenty-five 1-ounce candles is 25 candles * 0.1 ounces = 2.5 ounces.
Adding up the wax from the 20-ounce and 1-ounce candles, we have a total of 10 ounces + 2.5 ounces = 12.5 ounces of wax available.
To determine how many 5-ounce candles can be made, we divide the total available wax by the amount of wax needed for each 5-ounce candle:
Number of 5-ounce candles = Total available wax / Wax needed per 5-ounce candle
Number of 5-ounce candles = 12.5 ounces / 5 ounces
Number of 5-ounce candles ≈ 2.5 candles.
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PQ and QR are 2 sides of a regular 12-sided polygon
Answer:
Step-by-step explanation:
9. Find m DF
m
140°
DF:
=
E
44°
20. Find
mZPQR.
131*
m/POR=
Need done asap please show work
According to the angles between intersecting secant and tangent, the value of
angle DF is 52 degrees
angle PQR = 49 degrees
How to solve for angle DFThe value of angle DF is solved using the angles of intersecting secant out side the circle
The theorem give the formula in the form
44 = 1/2 (140 - DF)
88 = 140 - DF
DF = 140 - 88
DF = 52 degrees
Using intersection of tangents, for the second figure
exterior angle = 1/2 (major arc - minor arc)
major arc = 360 - 131 = 229
PQR = 1/2 (229 - 131)
PQR = 49 degrees
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I have a deck of 52 cards, from which I draw 3 cards and I would like to make a probability tree diagram, with two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade. I need a tree diagram which includes these branches and events.
The probability is solved and the tree diagram is given
Given data ,
The tree diagram to draw 3 cards out of 52 cards from the given probability details are:
The two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade.
_______ Draw a Spade _______
/ \
______/______ ______\_______
/ \ / \
/ \ / \
/ \ / \
Spade Not Spade Spade Not Spade
| | | |
Draw another Spade Not Draw a Spade Draw another Spade Not Draw a Spade
Hence , the probability of deck of cards is solved
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What is the range of f(x) = sin(x)?
the set of all real numbers -2pi≤y≤2pi
the set of all real numbers -1≤y≤1
the set of all real numbers 0≤y≤2pi
the set of all real numbers
Answer:
the set of all real numbers -1≤y≤1
Step-by-step explanation:
according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.
Please help me right now!
Thank you so much
The length of the arc KL in the given circle is 3.49 units
How to find the length of the arc KL?In a circle whose radius is R, the length of an arc defined by an angle x is given by:
Length = (x/360)*2*3.14*R
Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:
Length = (100/360)*2*3.14*2
Lenght = 3.49 units.
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The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
Snowfall Amount
Length of Snowfall
(hours)
Amount of Snow on the Ground
(inches)
0
3.3
0.5
4.5
1.0
5.7
1.5
6.9
2.0
8.1
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
The average rate of change for the snowfall amount is given as follows:
2.4 inches per hour.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
The change in the output is given as follows:
8.1 - 3.3 = 4.8.
(output is the amount of snow).
The change in the input is given as follows:
2 - 0 = 2.
(input is the time in hours).
Hence the average rate of change of the snowfall over time is given as follows:
4.8/2 = 2.4 inches per hour.
(change in the snowfall divided by the change in time).
Missing InformationThe table is given by the image presented at the end of the answer.
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Gabrielle is 13 years older than Mikhail. The sum of their ages is 97. What is Mikhail's age?
Answer: 42
Step-by-step explanation:
The best way to solve this is to set up an equation. In this problem, we can use "x" for Mikhail's age, so that Gabrielle's age becomes "x+13." Now, we can write, "x+x+13=97," because Mikhail's age (x) plus Gabrielle's age (x+13) is equal to 97. When we solve for x, we get x=42, so Mikhail's age is 42.
graph the function
X+6, X ≤-2
f(x)= x², -2≤ x ≤ 1.
-2x, x > 1
Answer:
Step-by-step explanation:
To graph the function, we'll break it down into three parts based on the given conditions.
For x ≤ -2:
The function f(x) = x + 6 is valid in this range. We'll plot a straight line with a slope of 1 and a y-intercept of 6. Since x ≤ -2, we'll extend the line towards the left indefinitely.
For -2 ≤ x ≤ 1:
The function f(x) = x² is valid in this range. We'll plot a curve representing a quadratic function. The graph starts at the point (-2, 4), curves upward, and ends at the point (1, 1).
For x > 1:
The function f(x) = -2x is valid in this range. We'll plot a straight line with a negative slope of -2. Since x > 1, we'll extend the line towards the right indefinitely.
Combining these three parts, we get the graph of the function as follows:
23(2+2+3+372+27272+"
A hemisphere is on top of a cylinder the radius of the hemisphere is 5 and the height of the cylinder is 8 what is the volume somehelp?
Answer:
V = π(5^2)(8) + (4/3)π(5^3)
= 200π + (500/3)π = (1,100/3)π
= about 1,151.92 cm^3
PLEASE HELP
The triangle above has the following measures.
q = 6 yd
m/Q=43°
Find the length of side r.
Round to the nearest tenth and include correct units.
Show all your work.
Answer:
r=5.9
Step-by-step explanation: