Answer:
Width is 10
Length is 18
Step-by-step explanation:
Perimeter is calculated as 2(w+l) or w+w+l+l. When you put those two numbers into the equation 2(10+18) or 10+10+18+18, you get the exact same answer of 56, and since 10 is eight less than 18, it would be the width.
Answer:
Length L = 18 m Width W = 10 m
Step-by-step explanation:
perimeter P = 2L + 2W
where
Perimeter P = 56 m
Width W = L - 8 m
find:
length L
width W
solution:
just plugin the values into the formula:
P = 2L + 2W
56 = 2L + 2(L - 8)
56 = 2L + 2L - 16
56 + 16 = 4L
L = 72/4
L = 18 m
solve for W:
substitute L=18 back into the equation W=L-8
W = 18 - 8
W = 10 m
therefore:
length L = 18 m
Width W = 10 m
proof:
56 = 2(18) + 2(10)
56 = 36 + 20
56 = 56 ----- OK
which ones are in scientific notation? 15 points
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the scale factor?
a. 0.08
b. 1.08
c. 0.92
d. 8
The scale factor after one year of depreciation is 0.92.(option-c)
The depreciation rate of 8% per year means that the car loses 8% of its value each year. To find the scale factor, we need to determine how much of the original value remains after one year of depreciation.
If the car loses 8% of its value each year, then the remaining value after one year is:
100% - 8% = 92% of the original value
We can express this as a decimal by dividing 92% by 100%, which gives:
92%/100% = 0.92
This means that the value of the car is 0.92 times its original value after one year of depreciation.
We can also check our answer by calculating the value of the car after one year:
Value after one year = 0.92 * $15,000 = $13,800
This is the expected value of the car after one year of depreciation, which confirms that our scale factor of 0.92 is correct.
Therefore, the answer is (C) .
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What would be the perimeter of this figure?
Answer:
40.9ft
Step-by-step explanation:
The perimeter is when you add all the sides together.
8 + 10 + 10 + 4 + 8.9 = 40.9ft
What is the value of y when x = 5 in the equation y = 5x?
The mean of ten numbers is 5. When another number is added the mean is still 5. What is the missing number?
Answer:
5
Step-by-step explanation:
Answer:
The answer is 5
Step-by-step explanation:
Last year, 9 employees of an electronics company retired. Their ages at retirement are listed below.
51, 61, 62, 54, 68, 58, 60, 57, 54
Find the mean retirement age.
6(m-1)=3(3m+5)
what does m=
Answer:
m = - 7
Step-by-step explanation:
Given
6(m - 1) = 3(3m + 5) ← distribute parenthesis on both sides
6m - 6 = 9m + 15 ( subtract 9m from both sides )
- 3m - 6 = 15 ( add 6 to both sides )
- 3m = 21 ( divide both sides by - 3 )
m = - 7
Choose the slope and y-intercept that
correspond with the graph.
Click on the correct answer
What is the value of x in 5x - 4 = 7x + 8?
Answer:
x = -6
Step-by-step explanation:
To find the value of x in the given equation, we have to solve for x.
5x - 4 = 7x + 8
Add 4 to both sides.
5x = 7x + 12
Subtract 7x from both sides.
-2x = 12
Divide both sides by -2.
x = -6
So the value of x would be -6.
I hope this helps. Happy studying.
Q: What is the value of x in 5x-4=7x+8
A: -6
SBS: 5x-4-7x=7x+8-7x -2x-4=8 -2x -4+4 --> 8+ 4-2x=12
(DIVIDE)
-2x/-2 = 12/-2= -6
4=[(43-34-32)*0]+2-2+4-3+5-2
Is this True?
Answer: True
Step-by-step explanation:
21.1w + 4.6 = 10.9w + 35.2
Answer:
25.7 = 46.1
Step-by-step explanation:
This question doesn't make sense but if it's true or false it's false
A number is missing the tens digit.
The number is 51 3 6.
What could the tens digit be if the number
is divisible by 2? By 4? By 8?
Answer:
The answer is 51,338
Step-by-step explanation:
Find the midpoint of points A(-7,7) and B(-1,-3)
Answer:
( −4,2)
Step-by-step explanation:
Use the midpoint formula to find the midpoint of the line segment.
exercise 10.6. golden ticket. a student was at work at the county amphitheater, and was given the task of cleaning 1500 seats. to make the job more interesting, his boss hid a golden ticket somewhere in the seats. the ticket is equally likely to be in any of the seats. let x be the number of seats cleaned until the ticket is found. calculate the expected value of x. round your answer to 1 decimal plac
The expected value of x is 750.5, rounded to 1 decimal place.
To calculate the expected value of x, we need to determine the probability distribution of x and then calculate the weighted average of x.
The probability of finding the golden ticket in the first seat cleaned is 1/1500, as there are 1500 seats and the ticket is equally likely to be in any of them.
Similarly, the probability of finding the ticket in the second seat cleaned is (1499/1500) * (1/1499) = 1/1500. The probability of finding the ticket in the third seat cleaned is (1499/1500) * (1498/1499) * (1/1498) = 1/1500, and so on.
From this pattern, we can observe that the probability of finding the ticket in the x-th seat cleaned is 1/1500.
Now, let's calculate the expected value of x:
E(x) = (1/1500) * 1 + (1/1500) * 2 + (1/1500) * 3 + ... + (1/1500) * 1500
E(x) = (1/1500) * (1 + 2 + 3 + ... + 1500)
E(x) = (1/1500) * [(1500 * 1501) / 2]
E(x) = (1501 / 2) = 750.5
Therefore, the expected value of x is 750.5, rounded to 1 decimal place.
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Any number or variable raised to the zeroth power is equal to what
Answer:
1
Step-by-step explanation:
Any number raised to the 0th power is 1, except for 0; 0 to the 0th power is undefined.
Answer:
[tex]\huge{\boxed{\sf{1}}}[/tex]
Step-by-step explanation:
Any number or variable raised to the 0 th power is equal to 1.
For example: If [tex]x^{0}[/tex] is an algebraic term, then [tex]x^{0}[/tex] =1. So, the value of the term having the index 0 is 1.
Hope I helped!
Best regards! :D
~TheAnimeGirl
8 gallons of gasoline cost $16.80. What is the price per gallon?
Answer:
$2.10/gallon
Step-by-step explanation:
8 gallons - $16.80
1 gallon - $2.10
Hope this helps!
Answer:
$2.10 per gallon
Step-by-step explanation:
Do
16.80/8 = 2.10
CHECK
2.10*8 = 16.80
find the linear approximation of the function g(x)=cube root of 1+x. Use it to approximate the numbers
cube root of 0.95
and cube root of 1.1
The linear approximation for g(x) = ∛(1+x) at a = 0 is g(x) = 1 + 0.33x.
Approximation for cube root of 0.95: 1.0165 Approximation for cube root of 1.1: 1.33The linear approximation of the function g(x) = cube root of 1+x at a = 0 is:
g(x) = 1 + 0.33x
To approximate the cube root of 0.95, we substitute x = -0.05 into the linear approximation. This gives us:
g(-0.05) = 1 + 0.33(-0.05) = 1.0165
Therefore, the cube root of 0.95 is approximately 1.0165.
To approximate the cube root of 1.1, we substitute x = 0.1 into the linear approximation. This gives us:
g(0.1) = 1 + 0.33(0.1) = 1.33
Therefore, the cube root of 1.1 is approximately 1.33.
Note that the linear approximation is only an approximation, and the actual values of the cube roots of 0.95 and 1.1 may be slightly different.
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to copy an angle using only a compass and a straightedge begin by marking the vertex of the new angle. then draw a ray from vertex which will be one of the legs of the new angle what is the next step in the construction?
Answer:
Set the compass to a convenient width, and draw an arc that is centered at the vertex of the original angle and intersects both legs of the original angle.
Step-by-step explanation:
Edmentum. Enjoy.. Don't get too tired yall, I love you and so does Christ Jesus.
consider the function h(x)= -2cos(8x-π/4)+5. what transformation results in j(x)=-2cos(8x-π/4)-5
The transformation from h(x) that gives j(x) is 10 units translation down
How to determine the transformation?The equation of the functions are given as
h(x) = -2cos(8x - π/4) + 5
j(x) = -2cos(8x-π/4) - 5
From the above equations, we can see that only the constant term of the equations are different
This means that the function h(x) is translated vertically to get the function j(x)
So, we simply subtract j(x) from h(x) to calculate the unit of translation
This is represented as
Units = j(x) - h(x)
This gives
Units = -2cos(8x - π/4) - 5 + 2cos(8x-π/4) - 5
Evaluate the like terms
Units = - 5 - 5
Evaluate the sum
Units = -10
This means that the transformation is 10 units translation downwards
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2 (t+2)
distributive
Answer:
A: 2t+4
Step-by-step explanation:
3. For what value of x is the equation 224 +7 = 2" true?
A. 2
B. 4
C. 11
D. 16
E. 44
Please lmk soon
Step-by-step explanation:
I think it's TRUE but the equation is false.
help with that
7.4 Find a subset of the vectors v₁ = (0, 2, 2, 4), v2 = (1, 0, -1, -3), 03 = (2, 3, 1, 1) and v1 V4 = (-2, 1, 3, 2) that forms a basis for the space spanned by these vectors. Explain clearly. (4) [
We need to find a subset of the vectors v₁ = (0, 2, 2, 4), v₂ = (1, 0, -1, -3), v₃ = (2, 3, 1, 1), and v₄ = (-2, 1, 3, 2) that forms a basis for the space spanned by these vectors. In this problem, we will perform the necessary calculations to determine the subset that forms a basis.
To find a subset of the given vectors that forms a basis for the space spanned by them, we need to check for linear independence among the vectors. We will start by considering all four vectors and then eliminate any redundant vectors.
We can construct an augmented matrix with the given vectors as columns:
[ 0 1 2 -2 ]
[ 2 0 3 1 ]
[ 2 -1 1 3 ]
[ 4 -3 1 2 ]
Applying row operations to the matrix, we can determine if any vectors can be eliminated due to linear dependence. After performing row operations, we find that the matrix is row equivalent to the following matrix:
[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
This indicates that all four vectors are linearly independent, and there are no redundant vectors. Therefore, the subset {v₁, v₂, v₃, v₄} forms a basis for the space spanned by these vectors.
Hence, the subset {v₁, v₂, v₃, v₄} is a basis for the space spanned by the given vectors.
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Suzy is making an apple pie and her recipe calls for 40 oz of apples at the grocery store apples are sold in pounds if there are 16 ounces in a pound how many pounds of apples should Suzy buy?
Answer: 2.5 lbs
Step-by-step explanation: Divide 40 by 16 to get the weight she needs.
Solve for X!!!
The equation is in the picture.
Answer:
x - 4 + 88 = 108
x + 84 = 108
x = 24
The correct answer is a.
Write the complex number in standard form. (Simplify your answer completely.) (5+ √5) (6-√-10)
To write the complex number (5+√5)(6-√-10) in standard form, we simplify the expression by multiplying the terms and then combine the real and imaginary parts. The standard form of the complex number is 30 + 5√2.
To simplify the expression (5+√5)(6-√-10), we need to multiply the terms using the distributive property.
First, let's multiply the real parts:
5 * 6 = 30.
Next, we multiply the imaginary parts:
√5 * -√-10 = -√(5 * -10) = -√(-50) = -√(50)(-1) = -√(25 * 2)(-1) = -√25 * √2 * (-1) = -5√2.
Now, let's combine the real and imaginary parts to write the complex number in standard form:
(5+√5)(6-√-10) = 30 + 5√2.
Therefore, the complex number (5+√5)(6-√-10) can be written in standard form as 30 + 5√2. In standard form, the complex number is expressed as the sum of a real part and an imaginary part. The real part is 30, and the imaginary part is 5√2.
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"In the 1980s, Tennessee conducted an experiment in which kindergarten students were randomly assigned to ""regular"" and ""small"" classes and given standardized tests at the end of the year. (Regular classes contained approxi- mately 24 students, and small classes contained approximately 15 students.) Suppose, in the population, the standardized tests have a mean score points and a standard deviation of 75 points. Let SmallClass denote variable equal to 1 if the student is assigned to a small class and eq otherwise. A regression of TestScore on SmallClass yields ... TestScore = 918.0 + 13.9 X SmallClass, R2 = 0.01, SER = 74.6. (1.6) (2.5) a. Do small classes improve test scores? By how much? Is the effect large? Explain. b. Is the estimated effect of class size on test scores statistically significant? Carry out a test at the 5% level. c. Construct a 99% confidence interval for the effect of SmallClass on TestScore. d. Does least squares assumption 1 plausibly hold for this regression? Explain."
a. This result is not significant. ; b. we reject the null hypothesis ; c.The 99% confidence interval for the effect of SmallClass on TestScore is (7.25, 20.55). ; d. The first assumption is plausibly valid for this regression.
a. Yes, small classes have been shown to enhance test scores, as per the analysis carried out. This means that students in smaller classes received an average of 13.9 more points on their tests than those in larger classes.
It is critical to note, however, that this result is not significant.
b. Carry out a test at the 5% level.
The null hypothesis will be H0: β1 = 0.
The alternative hypothesis will be H1: β1 ≠ 0.
This is a two-sided test with a 5% significance level.
Reject the null hypothesis if the t-statistic lies outside the interval (-2.5,2.5).
t-statistic= (13.9-0)/2.5
= 5.56 which is greater than 2.5.
Therefore, we reject the null hypothesis and conclude that the estimated effect of class size on test scores is statistically significant at the 5% level.
c. We know from the regression output that
b1= 13.9,
standard error of b1 (SEb1)= 2.5 and
degrees of freedom (df)= n-2
= 1636-2
= 1634.
The formula for the 99% confidence interval is given by:
Lower limit= 13.9- (2.58*2.5)
= 7.25
Upper limit= 13.9+ (2.58*2.5)
= 20.55
d. Least squares assumption 1 says that the model is linear in parameters.
The regression model
TestScore= 918.0+ 13.9 X
SmallClass is indeed linear in the parameters because we have a first-order linear model.
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Sam can do 120 jumping jacks in two minutes, how many jumping jacks can he complete in 5 mins.? (plz answer quick)
Answer:
300 jumping jacks
Step-by-step explanation:
120 ÷ 2 = 60 jumping jacks per minute
60 × 5 = 300 jumping jacks
Sam can do 300 jumping jacks in 5 minutes.
Hope that helps.
Answer:
60
Step-by-step explanation:
120 / 2 = 60 (jumping jacks per minute)
60 * 5 = 300
Best of Luck!
a) Geeta buys x apples, ( ) x+7 oranges and ( ) 2 1 x- bananas. The total number of pieces of fruit Geeta buys is 30. (i) Find the number of apples Geeta buys. ................................................. [3] (ii) The cost of one apple is 15 cents. The cost of one orange is 18 cents. The total cost of all the fruit is $5.55 . Find the cost, in cents, of one banana.
The cost of one banana is 3 cents.Given that Geeta buys x apples, x+7 oranges, and 2 1 x- bananas.The total number of pieces of fruit Geeta buys is 30.
(i) To find the number of apples Geeta buys, we need to form an equation based on the given information.x + x + 7 + 2(1 x-) = 30.Simplify and solve for xx + x + 7 + 2 - 2x = 30-x + 9 = 30x = 30 - 9x = 21.Therefore, the number of apples Geeta buys is 21.
(ii) Cost of 1 apple is 15 cents.Cost of 1 orange is 18 cents.The total cost of all the fruit is $5.55.Cost of 21 apples = 21 × 15 = 315 cents.Cost of (x + 7) oranges = (x + 7) × 18.Cost of 2 1 x- bananas = (2 1 x-) × y cents, where y is the cost of one banana.
Total cost = 315 + (x + 7) × 18 + (2 1 x-) × y= 555 cents.Equating the above equation, we get;315 + (x + 7) × 18 + (2 1 x-) × y= 555315 + 18x + 126 + 2y - 2x - y = 555.
Simplify the equation.16x + y = 114.Now, we need to find the value of y, which is the cost of 1 banana. Given that 21 bananas were already bought, and we need to find the cost of one banana only.
Therefore we need to subtract the cost of 21 bananas from the total cost of all fruit and then divide by the remaining number of bananas.114 - 2 1 x- × y = cost of bananas = (555 - 315 - 18x - 126) cents = 114 cents.Therefore, 2 1 x- × y = 114 - 21 × y y = 3.Hence, the cost of one banana is 3 cents.
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Which of the following pairs of trigonometric ratios is/are equal?
I. sin A and cos B
II. tan A and tan B III. cosec A and sec B A. I only B. II only C. I and II only
D. III only
E. I and III only
The pair of equal trigonometric ratios among the given options is tan A and tan B.
To identify the pair of equal trigonometric ratios among the given options, we have to use the basic identities of trigonometry.
Basic identities of trigonometry:1. sin² θ + cos² θ = 1 (Pythagorean identity)2. tan θ = sin θ/cos θ3. cot θ = cos θ/sin θ4. sec θ = 1/cos θ5. cosec θ = 1/sin θ.
Now, let's check the given options,I. sin A and cos B: Not equal because sin is opposite/hypotenuse and cos is adjacent/hypotenuse in a right-angled triangle.II. tan A and tan B:
Equal because the tan is opposite/adjacent in a right-angled triangle. III. cosec A and sec B: Not equal because cosec is hypotenuse/opposite and sec is hypotenuse/adjacent in a right-angled triangle.
Therefore, the correct answer is (B) II only. Hence, the main answer is B. II only.
The pair of equal trigonometric ratios among the given options is tan A and tan B.
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For problems 4-6, determine the outputs for the following inputs of the function: f(x) = -2x² + 12x-4 x=3 5) x=-4 6) x=0 For problems 7 & 8, write the equation of the line through the points given. 7) (-5,2) and (5,4) 8) (-3,8) and (1.-4)
For the function f(x) = -2x² + 12x - 4, we can find the outputs for specific inputs. When x = 3, the output is 14. When x = -4, the output is -84. When x = 0, the output is -4.
For finding the equation of a line passing through given points, the equation can be determined using the slope-intercept form, y = mx + b.
To determine the outputs of the function f(x) = -2x² + 12x - 4 for specific inputs, we substitute the given values of x into the function and calculate the corresponding outputs.
a) For x = 3: f(3) = -2(3)² + 12(3) - 4 = -18 + 36 - 4 = 14.
b) For x = -4: f(-4) = -2(-4)² + 12(-4) - 4 = -32 - 48 - 4 = -84.
c) For x = 0: f(0) = -2(0)² + 12(0) - 4 = 0 - 0 - 4 = -4.
Moving on to finding the equation of lines passing through given points:
7) The points given are (-5,2) and (5,4). We can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates, we have m = (4 - 2) / (5 - (-5)) = 2 / 10 = 1/5. Using the slope-intercept form, y = mx + b, we can substitute one of the given points and the slope to solve for b. Let's use the point (5,4): 4 = (1/5)(5) + b. Simplifying, we find b = 4 - 1 = 3. Therefore, the equation of the line is y = (1/5)x + 3.
The points given are (-3,8) and (1,-4). Calculating the slope, m = (-4 - 8) / (1 - (-3)) = -12 / 4 = -3. Again, using the slope-intercept form, we substitute the point (1,-4) and the slope: -4 = (-3)(1) + b. Solving for b, we find b = -1. Hence, the equation of the line is y = -3x - 1.
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