The temperature of 80°F is equivalent to 48°C.
How to convert temperature from Fahrenheit to Celsius using a specific formula?To convert 80°F to Celsius degrees using the formula C = (F - 32), we substitute the given Fahrenheit temperature into the formula.
C = (80 - 32) = 48
Therefore, the temperature of 80°F is equivalent to 48°C.
The Celsius scale is commonly used in scientific and international contexts, while the Fahrenheit scale is more prevalent in the United States. The conversion formula allows us to convert temperatures between these two scales.
Rounding to the nearest tenth of a degree, we find that 48°C remains unchanged.
It's worth noting that the Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C at standard atmospheric pressure. In contrast, on the Fahrenheit scale, water freezes at 32°F and boils at 212°F.
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A recipe for maroon paint says, "mix 5 ml of red paint with 3 ml of blue paint."
use snap cubes to represent the amounts of red and blue paint in the recipe. then, draw a sketch of your snap-cube representation of the maroon paint.what amount does each cube represent?
Assuming that one snap cube represents one milliliter (ml) of paint, we can use five red snap cubes to represent 5 ml of red paint and three blue snap cubes to represent 3 ml of blue paint. We can arrange these snap cubes in a row to represent the recipe:
RRRRR BBB
This indicates that we mix 5 ml of red paint with 3 ml of blue paint to create the maroon paint.
To draw a sketch of the snap-cube representation of the maroon paint, we can combine the red and blue snap cubes into a single row:
RRRRR BBB
This gives us a row of eight snap cubes, which represents the maroon paint. Visually, the maroon paint will appear as a blend of red and blue, with a darker, richer hue than either color alone.
Each snap cube represents one milliliter (ml) of paint. Therefore, in this representation, each snap cube represents a fixed amount of paint, regardless of the color. In other words, each cube represents a unit of volume, rather than a unit of color or pigment.
Qué expresión es igual a 4.6?
a. 1.6 + (3 × 4) – 2 ÷ 2
b. 1.6 + 3 × 4 – 2 ÷ 2
c. [1.6 + (3 × 4)] – (2 ÷ 2)
d. (1.6 + 3) × (4 – 2) ÷ 2
The correct expression that is equal to 4.6 is option c. [1.6 + (3 × 4)] – (2 ÷ 2)
Let's evaluate each expressions using the BODMAS rule of mathematics,
a. 1.6 + (3 × 4) – 2 ÷ 2
= 1.6 + 12 - 1
= 12.6
b. 1.6 + 3 × 4 – 2 ÷ 2
= 1.6 + 12 - 1
= 12.6
c. [1.6 + (3 × 4)] – (2 ÷ 2)
= [1.6 + 12] - 1
= 12.6
d. (1.6 + 3) × (4 – 2) ÷ 2
= 4.6 × 2 ÷ 2
= 4.6
BODMAS is an acronym used to remember the order of operations in mathematics: Brackets, Orders, Division, Multiplication, Addition, Subtraction. It is used to perform calculations in the correct order to obtain the correct result. Therefore, the correct answer is (c).
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Complete question - Which expression is equal to 4.6?
a. 1.6 + (3 × 4) – 2 ÷ 2
b. 1.6 + 3 × 4 – 2 ÷ 2
c. [1.6 + (3 × 4)] – (2 ÷ 2)
d. (1.6 + 3) × (4 – 2) ÷ 2
Find an exponential function that passes through (2,8) and (4,128)
The final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
To find an exponential function that passes through the points (2,8) and (4,128), follow these steps:
Step 1: Recall the general form of an exponential function: y = ab^x
Here, 'a' and 'b' are constants that need to be determined using the given points.
Step 2: Substitute the first point (2,8) into the equation:
8 = ab^2
Step 3: Substitute the second point (4,128) into the equation:
128 = ab^4
Step 4: Divide the second equation by the first equation to eliminate 'a':
(128 = ab^4) / (8 = ab^2)
16 = b^2
Step 5: Solve for 'b':
b = √16
b = 4
Step 6: Substitute the value of 'b' back into the first equation:
8 = a(4^2)
Step 7: Solve for 'a':
8 = 16a
a = 8/16
a = 1/2
Step 8: Write the final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
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Obtain the equation of the line that passes through the point (4 , 6) and is parallel to the line y= -2x+4.
Answer:
y = -2x + 14
Step-by-step explanation:
OK so first u have to do y = -2x + b cuz its parallel
then u gotta just plug in the ordered pair so
6 = -2(4)+b
6 = -8 +b
14 = b
So now u have to do
y = -2x + 14
Find the exact values of sin 2u, cos2u, and tan2u using the double-angle formulas cot u= square root 2, pi < u < 3pi/2
sin 2u = -1/2, cos 2u = -1/2, tan 2u = 1, because cot u = sqrt(2) and the range of u is between pi and 3pi/2.
How to find the trigonometric function?
Given cot u = sqrt(2) and the range of trigonometric of u, we can determine the values of sine, cosine, and tangent of 2u using the double-angle formulas. First, we can find the value of cot u by using the fact that cot u = 1/tan u, which gives us tan u = 1/sqrt(2). Since u is in the third quadrant (i.e., between pi and 3pi/2), sine is negative and cosine is negative.
Using the double-angle formulas, we can express sin 2u and cos 2u in terms of sin u and cos u as follows:
sin 2u = 2sin u cos u
cos 2u =[tex]cos^2[/tex] u - [tex]sin^2[/tex] u
Substituting the values of sine and cosine of u, we get:
sin 2u = 2*(-sqrt(2)/2)*(-sqrt(2)/2) = -1/2
cos 2u = (-sqrt(2)/2[tex])^2[/tex] - (-1/2[tex])^2[/tex] = -1/2
To find the value of tangent of 2u, we can use the identity:
tan 2u = (2tan u)/(1-[tex]tan^2[/tex] u)
Substituting the value of tan u, we get:
tan 2u = (2*(1/sqrt(2)))/(1 - (1/sqrt(2)[tex])^2[/tex]) = 1
Therefore, sin 2u = -1/2, cos 2u = -1/2, and tan 2u = 1.
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36 inches in 3 feet
rate=____ unit rate ___
Answer:
Rate: 36:3
Unit Rate: 12:1
Step-by-step explanation:
1. Un ciclista ha recorrido 145. 8 km en una etapa, 136. 65 km en otra etapa y 162. 62 km en una tercera etapa. ¿Cuántos kilómetros le quedan por recorrer si la carrera es de 1000 km?
Esta es una y la segunda es otra ayúdenme
2. Una clinica dental tiene una tarifa de $ 19,99 para las calzas de piezas dentales. Si en un mes se registraron 109 calzas realizadas, ¿ que cantidad de dinero ingreso a la clinica?
1) The distance left in the race is 554.93km
2) The total amount earned is $2,178.91
How many kilometers remain in the race?We know that the total race is of 1000km, to find the distance missing, we need to take that total distance and subtract the amounts that the cyclist already traveled.
Then we will get:
distance left = 1000km - 145.8km - 136.65km - 162.62 km
distance left = 554.93km
That is the distance left in the race.
2) We know that each piece costs $19.99, and 109 pieces are sold, then the amount earned is the product between these two numbers.
Earnings = 109*$19.99 = $2,178.91
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The shopkeeper sold every day the number of eggs is recorded. At equal intervals group 42, 49, 61, 35, 27, 36, 50, 34, 31, 40
The shopkeeper sold an average of 40.5 eggs per day during the given interval.
How to find the avg number of eggs?To calculate the average number of eggs sold per day, add up the total number of eggs sold and divide by the number of days.
Total number of eggs sold = 42 + 49 + 61 + 35 + 27 + 36 + 50 + 34 + 31 + 40 = 405
Number of days = 10
Average number of eggs sold per day = 405 / 10 = 40.5
The shopkeeper sold an average of 40.5 eggs per day during the given interval.
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The shopkeeper sold every day the number of eggs is recorded. At equal intervals group 42, 49, 61, 35, 27, 36, 50, 34, 31, 40
What is the average number of eggs sold per day by the shopkeeper over the given interval?
The money in Maya's college savings account earns 2 1/5% interest. Which value is less than 2 1/5%?
A. 0. 0215
B. 11/5
C. 0. 022
D. 11/500
A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.
= 2 1/5% / 100
= (2 + (1/5)) / 100
= 0.022
A value that is less than 0.022 from the given data is 0. 0215.
Therefore, a value less than 2 1/5% is 0. 0215.
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Use the given facts about the functions to find the indicated limit.
lim x->3 f(x)=0, lim x->3 g(x)=4 lim x->3 h(x)=2
lim x->3 6h/ 4f+g (x)
*there are no answer choices. Its a prompt*
The value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
Given, [tex]\lim_{x \to 3} f(x)=0[/tex]
[tex]\lim_{x \to 3} g(x)=4[/tex]
[tex]\lim_{x \to 3} h(x)=2[/tex]
We have to find the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex]
[tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)=\lim_{x \to 3} \frac{6h(x)}{4f(x)+g(x)}[/tex]
[tex]= \frac{\lim_{x \to 3}6h(x)}{\lim_{x \to 3}4f(x)+\lim_{x \to 3}g(x)}[/tex]
[tex]=\frac{6\times 2}{4\times0+4}[/tex]
= 12/4
= 3
Hence, the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
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someone help pls!! giving brainlist to anyone who answers
Answer: csc M = [tex]\frac{\sqrt{86} }{8}[/tex]
Step-by-step explanation:
The csc is related to sin
csc x = 1/sin x
find sin M first then flip it to find csc M
sin M= opposite/hypotenuse
sin M= [tex]\frac{8}{\sqrt{86} }[/tex] >flip that
csc M = 1/sin M
csc M = [tex]\frac{\sqrt{86} }{8}[/tex] >root cannot be simplified it breaks down into 2 and 43
which are 2 prime numbers
Kathleen has a fair die with 6 different-colored sides:red,yellow,blue,green,orange, and purple. She rolls the die 120 times. The die lands on the color green 18 times. Based on Kathleen's results, The experimental probability of rolling the color green is?
The Experimental probability of rolling the color green is 0.15
How to calculate the experimental probability of rolling the color green isThe experimental probability of rolling the color green can be calculated by dividing the number of times the die lands on green by the total number of rolls:
Experimental probability of green = Number of green rolls / Total number of rolls
Experimental probability of green = 18 / 120
Experimental probability of green = 0.15 or 15%
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Suppose we used a between subjects design to see if caffeine influenced levels of alertness. We had three groups of participants: participants who received 8 ounces of a caffeinated beverage, participants who received 24 ounces of a caffeinated beverage, and participants who received no caffeine. If this was a between subjects design with 30 total participants, how many participants would be in each condition
If we have 30 total participants in a between-subjects design with three groups, we can assign any number of participants to each group as long as the sum of participants in each group adds up to 30. The number of participants in each group is 10 in the 8-ounce group, 15 in the 24-ounce group, and 5 in the no-caffeine group.
If we have a total of 30 participants in a between-subjects design, we need to divide them into three groups according to the conditions.
Let x be the number of participants who received 8 ounces of a caffeinated beverage, y be the number of participants who received 24 ounces of a caffeinated beverage, and z be the number of participants who received no caffeine. Since we have a total of 30 participants, we can write
x + y + z = 30
We don't know the specific number of participants in each group, but we do know that they must add up to 30.
However, we also know that each participant can only be in one group, which means that we have mutually exclusive groups. Therefore, we can assume that there is no overlap between the groups, which means that the total number of participants in each group is
x + y + z = 30
z = 30 - (x + y)
So, we can assign any value to x and y, as long as the sum of x and y is less than or equal to 30. Then, we can find the value of z using the equation above.
For example, if we assign 10 participants to the 8-ounce group and 15 participants to the 24-ounce group, we would have
x = 10
y = 15
z = 30 - (10 + 15) = 5
So, there would be 10 participants in the 8-ounce group, 15 participants in the 24-ounce group, and 5 participants in the no-caffeine group.
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Below are the steps for copying Line Segment DE using dynamic geometry software. Which sequence has the steps in the correct order?
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Construct a circle centered at the point G with radius Line Segment DE.
3.) Line Segment DE ≅ Line Segment GH
4.) Draw a point and label it G.
~a.) 2,4,1,3
~b.) 4,2,1,3
~c.) 2,1,4,3
~d.) 3,4,2,1
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is in the order of 2,1,4,3. So, correct option is C.
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is:
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Draw a point and label it G.
3.) Construct a circle centered at the point G with radius Line Segment DE.
4.) Line Segment DE ≅ Line Segment GH
Therefore, option c.) 2,1,4,3 is the correct sequence of steps. The first step is to draw the original line segment DE with endpoint H on the circle.
The second step is to draw a point and label it G. The third step is to construct a circle centered at G with the same radius as Line Segment DE. Finally, in the fourth step, the line segment GH is drawn such that it is congruent to Line Segment DE, completing the copy of Line Segment DE.
So, correct option is C.
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The ratio of Adults to Girls in a tennis club is 5:1
The ratio of Girls to Boys in the same club is 3:4
What is the ratio of adults to boys?
The ratio of adult to boys is 35:24
What is ratio?A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. For example, if the ratio of boys to girls in a class is 4:1. This means that the for every 4 boys therefore is a girl.
Represent the total number of adult, boys and girls in the club by x
This means number of boys = 4/7× x
number of adult = 5/6 × x
Therefore the ratio of adults to boys will be
5x/6 : 4x/7
= 5/6 : 4/7
multiply through by 42
= 35 : 24
therefore the ratio of adult to boys is 35: 24
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to measure the length of a hiking trail, a worker uses a device with a 2-foot-diameter wheel that counts the number of revolutions the wheel makes. if the device reads 1,100.5 revolutions at the end of
the trail, how many miles long is the trail, to the nearest tenth of a mile?
The length of the trail is determined as 1.3 miles.
What is the length of the trail?The length of the trail is calculated as follows;
The circumference of the circle is calculated as;
S = πd
where;
d is the diameter of the circleS = π x 2 ft
S = 2π ft
I revolution = 1 circumference = 2π ft
1 rev = 2π ft
1,100.5 rev = ?
= 1,100.5 rev/rev x 2π ft
= 6,914.65 ft
5280 ft -------> 1 mile
6,914.65 ft ------> ?
= 1.3 miles
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Which expression is equivalent to 1/2(2n+6
1/2+2n+6
2 1/2 + 6 1/2
n + 6
n+ 3
A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μ and variance σ2 of a single roll are 3. 5 and 2. 92, respectively. What is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2?
The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.
The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.
The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0
The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)
where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.
Since each roll of the die is independent, the variance of the sample mean for each sample is given as:
σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584
σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292
Substituting these values in the above equation, we get:
σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468
Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:
σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)
Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.
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What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? x^2= -16x-37
The intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.
To complete the square for the given equation, we need to add a constant value to both sides of the equation such that we can factor the left-hand side as a perfect square.
x^2 + 16x = -37
To determine the constant value we need to add to both sides, we take half the coefficient of x (which is 16/2 = 8) and square it to get 64. Then we add 64 to both sides of the equation:
x^2 + 16x + 64 = 27
Now we can factor the left-hand side as a perfect square:
(x + 8)^2 = 27
So the intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.
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The altitude to the hypotenuse of a right angled triangle is 8 cm. If the hypotenuse is 20 cm long, find the lenghs of the two segments of the hypotenuse
On a certain hot summer's day,670 people used the public swimming pool. The daily prices are for children 1.25 and for adults.2.00 The receipts for admission totaled 1118.00 How many children and how many adults swam at the public pool that day
Based on simultaneous equations, the number of children and adults who swam at the public pool that hot summer's day is as follows:
Children = 296Adults = 374.What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Simultaneous equations are also referred to as a system of equations because the equations are solved at the same time.
The total number of people who used the public swimming pool = 670
The unit price for children = $1.25
The unit price for adults = $2.00
The total amount collected that day = $1,118
Let the number of children who swam at the public pool that day = x
Let the number of adults who swam at the pool that day = y
Equations:x + y = 670 ... Equation 1
1.25x + 2y = 1,118 ... Equation 2
Multiply Equation 1 by 2:
2x + 2y = 1,340 Equation 3
Subtract Equation 2 from Equation 3:
2x + 2y = 1,340
-
1.25x + 2y = 1,118
0.75x = 222
x = 296
y = 670 - 296
= 374
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How do I solve for X with the base numbers on a right triangle. (Please give an explanation and an answer, I need to know how it works.)
Let's label the 3 points as A;B;C, where BC is the hypotenuse and AB is the shortest side, and x as AH.
We can see that triangle AHC is similar to triangle CAB, and triangle ACH is similar to triangle BCA, so therefore triangle AHC is similar to triangle CHA (i might've messed up the order but you get it)
Because they are similar, we get the ratio : x/12 = 40/x, or x^2 = 480.
So, x = [tex]\sqrt{480}[/tex], or 21.9 (1 d.p)
Answer:
21.9 units-----------------------
According to the right triangle altitude theorem:
the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.We see x is the altitude and 12 & 40 are the segments formed on the hypotenuse.
Applied to the given triangle, we get following equation:
[tex]x=\sqrt{12*40} =\sqrt{480} =21.9\ units[/tex]Find the volume of the solid generated when the rectangle below is rotated about side
LO. Round your answer to the nearest tenth if necessary.
The volume of the obtained solid is 36 units³.
Given that a rectangle of dimension 9 units x 2 units, has been rotated to form a solid we need to find its volume,
So we know that a rectangle rotated to form a rectangular prism.
Volume of a rectangular prism = product of the dimensions.
The dimensions of the obtained solid will be 9 units x 2 units x 2 units,
So the volume = 9 x 2 x 2 = 36 units³
Hence the volume of the obtained solid is 36 units³.
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Solve 2x(x 0.5) = −(x+2.5)² + 5.5 by graphing. Round to the nearest thousandth.
x≈
and x
we find that the solutions to the equation are:x ≈ -1.283, x ≈ 4.283.
How to solve the equation ?To solve the equation 2x(x+0.5) = -(x+2.5)² + 5.5 by graphing, we can first rearrange it to the standard form:
x² - 3x - 2 = 0.5(x+2.5)²
Then we can plot the two functions y = x² - 3x - 2 and y = 0.5(x+2.5)² - 5.5 on the same graph and find their intersection points, which represent the solutions to the equation.
Enter the two functions in separate equations:
[tex]y_1 = x^2 - 3x - 2[/tex]
[tex]y_2 = 0.5(x+2.5)^2 - 5.5[/tex]
Adjust the zoom level and position of the graph to see the intersection points.
Click on the intersection points to see their coordinates.
Round the coordinates to the nearest thousandth.
After following these steps, we find that the solutions to the equation are:
x ≈ -1.283
x ≈ 4.283
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A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
The confidence level represents the degree of certainty that the interval contains the true population parameter.
The statement "determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520" means that if the farmer were to repeat the sampling process many times and calculate the confidence interval each time, 95% of those intervals would contain the true mean number of suitable apples per tree.
Therefore, we can be 95% confident that the true mean number of suitable apples produced per tree is within the interval of 375 to 520 for this particular sample of 40 trees.
The confidence level represents the degree of certainty that the interval contains the true population parameter.
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Andre owns a condominium with a value of $155,000. He has a stock portfolio worth $8,100. He owes $3,300 on his car, which is valued at $9,100. He has $7,600 in student loans to repay. He has a credit card balance of $4,327. He also has $2,600 in a bank account. Construct a net worth statement to find Andre's net worth.
Using net worth statement, Andre's net worth is $159,573.
How to Construct a net worth statement to find Andre's net worth.Andre's net worth can be calculated by subtracting his total liabilities from his total assets.
Total assets = $155,000 (condominium) + $8,100 (stock portfolio) + $9,100 (car value) + $2,600 (bank account) = $174,800
Total liabilities = $3,300 (car loan) + $7,600 (student loans) + $4,327 (credit card balance) = $15,227
Net worth = Total assets - Total liabilities = $174,800 - $15,227 = $159,573
Therefore, Andre's net worth is $159,573.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
What is the exact circumference of a circle with a radius of 15 cm?
Responses
10π cm
10 pi, cm
15π cm
15 pi, cm
30π cm
30 pi, cm
60π cm
Answer:
30π cm
Step-by-step explanation:
if r = 15 cm
circumference = π2r
= π × 2 × 15
= 30π cm
#CMIIWThe volume of a cylinder is twice the volume of a cone. The cone and the
cylinder have the same diameter. The height of the cylinder is 5 meters.
What is the height of the cone?
The height of the cone that the volume of a cylinder is twice the volume of a cone is 7.5 meters.
How to determine the height of the coneLet's first define some variables to represent the dimensions of the cone and cylinder. Let's use r for the radius of both shapes, h for the height of the cone, and 5 for the height of the cylinder.
The volume of a cone is given by V_cone = (1/3)πr^2h, and the volume of a cylinder is given by V_cylinder = πr^2h.
We are told that the volume of the cylinder is twice the volume of the cone:
V_cylinder = 2V_cone
Substituting the formulas for the volumes of the cone and cylinder, we get:
πr^2(5) = 2[(1/3)πr^2h]
Simplifying, we can cancel the π and the r^2 terms on both sides:
5 = (2/3)h
Multiplying both sides by 3/2, we get:
h = 7.5
Therefore, the height of the cone is 7.5 meters.
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A rectangular prism has a square
base with edge length (x + 1). Its
volume is (x + 1)2(x – 3). What
does the expression (x + 1)(x – 3)
represent?
area of the base
area of one side
height of the prism
surface area of the prism
The expression (x + 1)(x - 3) represents the Area of base of the prism.
What is Prism?a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.
According to question:The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).
We can find the height of the prism by dividing the volume by the area of the base:
B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)
Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.
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