Answer:
Pretty sure the answer is 20 :)
Answer:
20 inches
Step-by-step explanation:
From the question, diagonal of the television screen is given to be 25 inch and the width of the television set is given to be 15 inches and we are asked to find the height of the screen.
We can solve this question using the Pythagoras theorem.
The Pythagoras theorem states that in a right-angle triangle;
opposite² + adjacent² = hypotenuse²
From the question, the width is given to be 15 inches, the with is our adjacent. Also the diagonal is given to be 25 inches, the diagonal is our hypotenuse. And we were ask to find the height, the height is our opposite.
so;
opposite = ?
adjacent = 15
hypotenuse = 25
Let opposite = x
we can now substitute into our theorem;
opposite² + adjacent² = hypotenuse²
x² + 15² = 25²
x² = 25² - 15²
x² = 625 - 225
x² = 400
x = √400
x = 20
opposite = 20 inches
Since opposite is the height of the screen, then the height of the screen is 20 inches.
Therefore the height of the screen is 20 inches.
A large soup pot holds 20 quarts. What could be its volume in liters?
Answer:
In litres the volume of the pot of soup is 18.93litre
Step-by-step explanation:
This problem seeks to examine our understanding of unit conversion
Step one
Convert quarts to liters
Definition of quart (symbol: qt)
Quart is a unit of volume in the United States customary and imperial systems of measurement. Multiple.
Step two
If 1 qt=0.946353 litre
20qt=x litre
By cross multiplication we have
x litre = 20*0.946353 litre
x=18.93litre
In litres the volume of the pot of soup is 18.93litre
To convert 20 quarts to liters, you would use the conversion factor of 1 liter equating to 1.06 quarts. Following this conversion, the volume of the soup pot would be approximately 18.87 liters.
Explanation:You're asked about the volume of a soup pot that contains 20 quarts and wants it to be converted to liters. Based on our comparison, 1 liter is approximately equivalent to 1.06 quarts. So to convert from quarts to liters, you'd divide the amount in quarts by the conversion factor.
Here is a step-by-step process to convert 20 quarts to liters:
Identify the conversion factor: 1 liter = 1.06 quarts
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85 students went on a field trip. three buses were filled and 25 students traveled in cars. how many students were in each bus?
Answer:
28 students
Step-by-step explanation:
you get 28.3 if you divide 85 by 3
Find the solution for -2y + 10 < -14.
1 y > -12
2 y < -12
3 y > 12
4 y < 12
Answer:
y > 12Step-by-step explanation:
[tex]-2y+10<-14\qquad\text{subtract 10 from both sides}\\\\-2y+10-10<-14-10\\\\-2y<-24\qquad\text{change the signs}\\\\2y>24\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}>\dfrac{24}{2}\\\\y>12[/tex]
the mean amount of money spent per week on gas by a sample of 25 drivers was found to be $57.00 with a standard deviation of $2.36. assuming the population distribution is normally distributed construct and interpret a 90% confidence interval for the mean amount of money spent on Gas per week
Answer:
See below
Step-by-step explanation:
To construct a confidence interval we use the following formula:
ci = (sample mean) +- z*(sd)/[n^(1/2)]
The sample mean is 57, the standard deviation is 2.36, n s 25 and z is the upper (1-C)/2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C)/2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:
ci = 57 +- 1.65*(2.36)/[25^(1/2)]
ci = 57 +- 3.894*/(5) = 57 +- 0.78
ci => (56.22 , 57.78)
associated press online provided information from a fiscal analyst stating that during the past 20 years, the average after tax income of the wealthiest 1% of americans had grown from $263,700 to $677,900. what was the percent increase? Round to the nearest percent.
Answer:
The percent increase is 157%
Explanation:
Average after tax income 20 years before: $263,700
Average after tax income after 20 years: $677,900
Increased average after tax income : $677,900-$263,700
=$414,200
Hence,
Percent increase = [tex]\frac{Increased amount}{original amount} \times 100[/tex]
=[tex]\frac{414,200}{263,700} \times 100[/tex]
=157.07%
After Rounding off:
=157%
157% is the percent increase
What is the simplified form of
(X/3-y/4)/(x/4+y/3) ? (6 points)
Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer
Step-by-step explanation:
Given fraction is:
[tex]\frac{\frac{x}{3}-\frac{y}{4}}{\frac{x}{4}+\frac{y}{3}}[/tex]
To solve the fraction, Taking LCM in denominator and numerator
[tex]=\frac{\frac{4x-3y}{12} }{\frac{3x+4y}{12}}[/tex]
When the numerator and denominator both have fractions, the simplified form is obtained be multiplying the numerator with reciprocal of the denominator. So,
[tex]= \frac{4x-3y}{12} * \frac{12}{3x+4y}\\=\frac{4x-3y}{3x+4y}[/tex]
Hence,
Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer
Keywords: fractions, simplification
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what is 139.5 as a fraction?
Answer:
139.5/1 or 1395/10
Step-by-step explanation:
The product of two consecutive even integers is 440.. what are the positive and negative integers?
Positive integers are 20,22 and negative integers are -22,-20.
Step-by-step explanation:
Let,
2 positive integers are x, x+2
According to given statement;
[tex]x(x+2)=440\\x^{2}+2x=440\\x^{2}+2x-440=0\\x^{2}+22x-20x-440=0\\x(x+22)-20(x+22)=0\\(x+22)(x-20)=0\\Either,\\x+22=0\\x=-22\\Or,\\x-20=0\\x=20[/tex]
If x=-22
Then,
x+2 = -22+2 = -20
Or,
x=20
x+2 = 20+2 = 22
Positive integers are 20,22 and negative integers are -22,-20.
Keywords: Integers, Multiplication
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The two consecutive even integers whose product is 440 are 20 and 22. When considered as positive and negative, they are +20 and -20, +22 and -22, respectively.
Explanation:To find the two consecutive even integers whose product is 440, we need to employ some algebraic reasoning. Let's denote the first of the two consecutive even integers as x.
Given that even integers follow a pattern of +2, we can denote the next consecutive even integer as x + 2.
Hence, we're solving for the equation x * (x + 2) = 440. Solving this equation will give us our consecutive even integers, which are 20 and 22. In terms of positive and negative integers, they would be represented as +20 and -20, +22 and -22, respectively.
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PLEASE HELP ASAP!!!
Which of these sentences is an independent clause?
1. While Marvin plays air guitar in the back seat.
2. Unless she can get the gum out of her hair in time for the big dance.
3. The superhero is afraid of heights.
4. Until Thanksgiving is over.
Answer:
3. The superhero is afraid of heights.
"The superhero is afraid of heights." is independent clause because the sentence contains a subject and verb and it's a complete sentence.
Step-by-step explanation:
An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence.
Jim studied in the Sweet Shop for his chemistry quiz.
A dependent clause is a group of words that contains a subject and verb but does not express a complete thought. A dependent clause cannot be a sentence. Often a dependent clause is marked by a dependent marker word. A dependent marker word is a word added to the beginning of an independent clause that makes it into a dependent clause. Some common dependent markers are: after, although, as, as if, because, before, even if, even though, if, in order to, since, though, unless, until, whatever, when, whenever, whether, and while.
When Jim studied in the Sweet Shop for his chemistry quiz . . .
(What happened when he studied? The thought is incomplete.)
Hope this helps!!!Answer: choice 3. The superhero is afraid of heights
The other choices are sentences that are incomplete because they need more structue to them. For example, sentence 1 implies that something else is going on during Marvin's guitar time. The other sentences have cliffhangers as well and they arent fully independent or on their own. Sentence 3 expesses a single complete thought without introducing some other related or tangential thought needed to complete that idea.
PLEASE HELP ME SOLVE THIS 7TH GRADE MATH PROBLEM, THANK YOU!
Answer:
The correct answer is s = 27.
Step-by-step explanation:
This problem already gives us an equation so all we need to do is plug in the numbers:
c = 39.95 + 0.15(s + r) becomes 53.45 = 39.95 + 0.15(s + 63). Now to solve:
53.45 = 39.95 + 0.15(s + 63)
13.50 = 0.15(s + 63) Subtract 39.95 from both sides
13.50 = 0.15s + 9.45 Distribute 0.15 to s and 63
4.05 = 0.15s Subtract 9.45 from both sides
27 = s Divide both sides by 0.15
Hope this helps,
❤A.W.E.S.W.A.N.❤
June uses 12 eggs to make cupcakes. She uses 4 eggs for each batch of
cupcakes. Which expression can be used to find the number of batches she
makes?
12 - 4
12 +4
12:4
12 x 4
Done
Answer:
12/4=3
Step-by-step explanation:
12/4
The expression that could be used to find the no of batches she makes is [tex]= 12\div 4[/tex]
Given that,
June uses 12 eggs to make cupcakes. She uses 4 eggs for each batch of cupcakes.Based on the above information, the calculation is as follows:
[tex]= 12\div 4[/tex]
= 3
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write a syarem of linear equations that defines the verbal problem, and then answer the question.
a rectangular pasture has a perimeter of 1000 feet. the pastures length is 300 feet more than its width.
whats the area of the pasture?
Answer:
40,000 ft
Step-by-step explanation:
The area of a rectangle is weight*length, and the perimeter is the sum og the four sides, which are 2 lengths sides ans 2 width sides, so:
area = w*l
perimeter = 2w + 2l
If the perimeter is 1000 ft:
2w + 2l = 1000
Also, the length is 300 ft more than width, so:
l = 300 +w
So, our system is:
2w + 2l = 1000 (equation 1)
l =300 + w (equation 2)
Son, we can solve it by replacing equation 2 in equation 1:
2w + 2(300 +w) = 2w + 600 + 2w = 4w + 600 = 1000
Now, subtract 600 in both sides:
4w + 600 - 600 = 1000 - 600
4w = 400
Divide both sides by 4:
4w/4 = 400/4
w = 100
Lets replace this w value in equation 2 to find l:
l = 300 + 100 = 400, so l=400
Finally we can find the area using the area formula:
area = 400*100 = 40,000 ft2
So, the area is 40,000 ft2
Final answer:
The area of the pasture is found by setting up and solving a linear system (1000 = 2w + 2(w + 300)); the dimensions of the rectangle are found to be 100 feet in width and 400 feet in length. The area is then calculated by multiplying the width by the length, yielding an area of 40,000 square feet.
Explanation:
To solve the problem, we need to establish a system of linear equations to find the dimensions of the pasture. Given that the perimeter of a rectangle is 2 times the width plus 2 times the length (P = 2w + 2l), and the length is 300 feet more than its width (l = w + 300), we can set up the following equations:
P = 2w + 2l
l = w + 300
Since we know the perimeter is 1000 feet, we substitute this value into the first equation:
1000 = 2w + 2(w + 300)
1000 = 2w + 2w + 600
1000 = 4w + 600
400 = 4w
w = 100 feet
Once we have the width, we can substitute this into the second equation to find the length (l):
l = 100 + 300
l = 400 feet
To find the area of the pasture, we multiply the width by the length:
Area = width × length = 100 feet × 400 feet = 40,000 square feet
The area of the pasture is 40,000 square feet.
6.43999001x10^8 in standard form
Answer:
643999001
Step-by-step explanation:
kim is saving monyfor a trip this summer. She already has some money in her savings account and will add the same amount to her account each week. At the end of 2 weeks, Carla has $130. At the end of 8 weeks, she has $280. Write a linear function in the form y = mx + b to represent the amount of money, m, that Carla has saved after w weeks.
The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80
Step-by-step explanation:
Carla is saving money for a trip this summer. She already has some money in her savings account and will add the same amount to her account each week
At the end of 2 weeks, Carla has $130At the end of 8 weeks, she has $280Write a linear function in the form y = m x + b to represent the amount of money, m, that Carla has saved after w weeks
The linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are 2 points on the line
∵ The slope is the rate of change of y and x
∴ The same amount of money that Carla add every week = m
∵ At the end of 2 weeks, Carla has $130
∴ The first point is (2 , 130)
∵ At the end of 8 weeks, she has $280
∴ The second point is (8 , 280)
∵ [tex]m=\frac{280-130}{8-2}=\frac{150}{6}=25[/tex]
∴ The same amount of money that Carla add every week = $25
∵ The amount of money that Carla saved after w week is m
∴ m = 25 w + b, where b is the initial amount of money that she
saved in her account
To find b substitute w and m by the coordinates of one of the two
given points, let us use the first point
∵ w = 2 and m = 130
∵ m = 25 w + b
∴ 130 = 25(2) + b
∴ 130 = 50 + b
- Subtract 50 from both sides
∴ 80 = b
∴ m = 25 w + 80
The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80
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What decimal is equal to 4/25
Answer:
0.16
Step-by-step explanation:
Use long division
Answer:
0.16
Step-by-step explanation:
4÷25 = 0.16
10x - 26y=-38
6x + 13y=28
Answer:
[tex]\displaystyle [\frac{9}{11}, 1\frac{111}{143}][/tex]
Step-by-step explanation:
{10x - 26y = −38
{6x + 13y = 28
½[10x - 26y = −38]
{5x - 13y = −19 >> New Equation
{6x + 13y = 28
___________
[tex]\displaystyle \frac{11x}{11} = \frac{9}{11}[/tex]
[tex]\displaystyle x = \frac{9}{11}[/tex][Plug this back into both equations above to get the y-coordinate of 1 111⁄143]; [tex]\displaystyle 1\frac{111}{143} = y[/tex]
I am joyous to assist you anytime.
-7(2x - 4) - 7= 3(x - 5)+ 4x - 9 distribute and combine like terms
The largest cross-section of the sphere shown has an approximate area of 28.27 cm2, what is the approximate volume of the sphere? A) 14.14 cm3 B) 113.1 cm3 C) 226.2 cm3 D) 904.78 cm3
Answer:
B) 113.1 cm³
Step-by-step explanation:
The cross-section of a sphere is a circle. The area of a circle is:
A = πr²
The largest cross section passes through the center of the sphere, where the radius of the circle equals the radius of the sphere.
28.27 = πr²
r = 3.00
The volume of the sphere is therefore:
V = 4/3 π r³
V = 4/3 π (3.00)³
V = 113.1
Answer:
B
Step-by-step explanation:
need help with this !! will mark as brainliest
Answer:
AB = 9.6 cm
Step-by-step explanation:
ΔAPQ and ΔABC are similar triangles, thus ratio of corresponding sides are equal, that is
[tex]\frac{AP}{AB}[/tex] = [tex]\frac{PQ}{BC}[/tex], substitute values
[tex]\frac{8}{AB}[/tex] = [tex]\frac{10}{12}[/tex] ( cross- multiply )
10AB = 96 ( divide both sides by 10 )
AB = 9.6 cm
The adjacent sides of a parallelogram measure 11 cm and 5cm, and one angle measure 50 °6’. Find the area of the parallelogram
Answer:
42.5 square centimeters
Step-by-step explanation:
The area of the parallelogram is
[tex]A=a\cdot b\cdot \sin \alpha,[/tex]
where a and b are adjacent sides and [tex]\alpha[/tex] is inckuded angle.
In your case,
[tex]a=11\ cm\\ \\b=5\ cm\\ \\ \alpha=50^{\circ}6'[/tex]
Thus,
[tex]A=11\cdot 5\cdot \sin 50^{\circ}6'\approx 42.5\ cm^2[/tex]
solve using substitution -9x+7y=-15 and -8x+y=18
Answer:
x=-3, y=-6. (-3, -6).
Step-by-step explanation:
-9x+7y=-15
-8x+y=18
------------------
y=18-(-8x)=18+8x=8x+18
----------------------------------
-9x+7(8x+18)=-15
-9x+56x+126=-15
47x+126=-15
47x=-15-126
47x=-141
x=-141/47
x=-3
-8(-3)+y=18
24+y=18
y=18-24=-6
x=-3, y=-6.
Answer:
x = 51/28
y= 24/7
Step-by-step explanation:
Which point is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2)?
(4,0)
(-2,0)
(0,2)
(4-2)
Answer:
(4,0) and (-2,0)
Step-by-step explanation:
(x-4)(x+2)
one of the brackets must equal zero; hence, we equal each brakcet to zero and solve the equation.
x-4=0
x=4
__________________________________
x+2=0
x=-2
To lay this out in coordinate format we would get:
(4,0) and (-2,0)
so our answers are the first and second option.
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95cents, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 30 cups of coffee, using 464 ounces of coffee, while collecting a total of $37.20. How many cups of each size did Kyle fill?
Answer:
4, 16 and 10
Step-by-step explanation:
Here we would like to work with a system of 3 equations, we need ti find them. Lets call s the 10oz coffees, m the 14oz and l the 20oz.
As Kyle sold $37.2 selling 3 different types of coffee at their respective prices we can say:
revenue = s*0.95 + m*1.15 + l*1.5 = 37.2 [equation 1]
And as he sold 30 cups:
s + m + l = 30 [equation 2]
And as the total volume of coffee is 464 oz:
s*10 + m*14 + l*20 = 464 [equation 3]
So, we have a system of 3 equations with three unknowns s, m and l.
Take the eq 2 and subtract m and l in both sides:
s = 30 - m - l
Now, take it and replace in the other 2:
(30 - m - l)*10 + 14m + 20l = 464 [eq 3]
0.95(30 - m - l) + 1.15m + 1.5l = 37.2 [eq 1]
Working with equation 3:
300 -10m -10l + 14m + 20l = 464
300 + 4m + 10l = 464
4m + 10l = 164 [equation 3']
Now with eq 1:
0.95(30 - m - l) + 1.15m + 1.5l = 37.2
28.5 - 0.95m - 0.95l + 1.15m + 1.5 l = 37.2
28.5 + 0.2m + 0.55l = 37.2
0.2m + 0.55l = 8.7 [equaiton 1']
Now we passed to a 2-equation system with eq 1' and eq 3'.
Take eq 3' and subtract 4m in both sides:
10l = 164 - 4m
Now divide by 10 in both sides
l = [164 - 4m]/10
Now, with this value for l replace in eq 1':
0.2m + 0.55 ( [164 - 4m]/10) = 8.7
0.2m + 0.055 (164 - 4m) = 8.7
0.2m + 9.02 - 0.22m = 8.7
- 0.02m = -0.32
m = -0.32/-0.02
m = 16 ----> 16 14oz coffees
Now replace m=16 in eq 1' or 3' to find l:
4m +10l = 164
64 + 10l = 164
10l = 100
l = 10 ----> 10 20oz coffees
So, finally we replace l=10 and m=16 in equaiton 2:
s + m + l = 30
s + 16 +10 = 30
s = 30 - 26
s = 4
So, Kyle filled 4 10oz coffes, 16 14oz coffees and 10 20oz coffees.
What is 4(2a) + 7(-4b) + (3•c•5) writing in standard form
Answer:
8a-28b+15c
Step-by-step explanation:
4(2a)+7(-4b)+(3*c*5)
8a-28b+15c
6 (1/3x + 1/2 ) = 2x + 3 solve please:(
Answer:
Infinitely many solutions. The value of x can be any real number.
Step-by-step explanation:
6 times 1/3x = 2x
6 times 1/2 = 3
6 times (1/3x + 1/2) = 2x+3
The left side of the original equation becomes 2x+3. The right side is also 2x+3. Both sides are the same, so we get infinitely many solutions.
We have,
[tex]6(\frac{1}{3}x+\frac{1}{2})=2x+3[/tex]
First distribute 6 through parentheses
[tex]2x+3=2x+3[/tex]
We can see both sides are equal hence for all x the equation will result with tautology (undeniable equality).
The answer is [tex]x \in \mathbb{R}[/tex].
Hope this helps.
Question 2
In the diagram, BCD is a straight line. AD = 2V3 cm
Work out the exact length of CD. Give your answer in the form
a + bv3 where a and b are integers
Not drawn
accurately
2V3 cm
Answer:
[tex]CD=(3-\sqrt{3})\ cm[/tex]
Step-by-step explanation:
step 1
Find the length side AB
In the right triangle ABD
[tex]sin(30\°)=\frac{AB}{AD}[/tex]
[tex]AB=sin(30\°)(AD)[/tex]
we have
[tex]AD=2\sqrt{3}\ cm[/tex]
[tex]sin(30\°)=\frac{1}{2}[/tex]
substitute
[tex]AB=\frac{1}{2}(2\sqrt{3})[/tex]
[tex]AB=\sqrt{3}\ cm[/tex]
step 2
Find the length side BD
In the right triangle ABD
[tex]cos(30\°)=\frac{BD}{AD}[/tex]
[tex]BD=cos(30\°)(AD)[/tex]
we have
[tex]AD=2\sqrt{3}\ cm[/tex]
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]BD=\frac{\sqrt{3}}{2}(2\sqrt{3})[/tex]
[tex]BD=3\ cm[/tex]
step 3
Find the length side BC
In the right triangle ABC
we know that
BC=AB -----> is an 45°-90°-45° triangle
therefore
[tex]BC=\sqrt{3}\ cm[/tex]
step 4
Find the length side CD
we know that
[tex]BD=BC+CD\\CD=BD-BC[/tex]
substitute the values
[tex]CD=(3-\sqrt{3})\ cm[/tex]
find the value of x
17
12
10
14
what is highest common factor of 98 and 42
Answer:
So the greatest common factor 42 and 98 is 14.
Calculate the percent error
1. Jerri estimates that 30 people would attend the dinner event but only 25 people attended.
2. Gene estimated the length of the fence to be 150 feet, but the actual measurement was 142 feet.
Answer:
Therefore, the percent error in 1. 20%
and the percent error in 2. 6%
Step-by-step explanation:
Given:
1. In estimation of 30 people only 25 people attended.
2. In estimated length of 150 feet the measurement was 142 feet.
Now, in first case for the percent error we would calculate the difference between the people attended:
[tex]30-25=5[/tex]
And then, we will get the percentage error :
[tex]\frac{5}{25} \times 100[/tex]
[tex]\frac{500}{25}[/tex][tex]=20[/tex].
Therefore, the percentage error is 20%.
Now, in second case for the percent error we would repeat the above process as done in first case:
[tex]150-142=8[/tex]
And then:
[tex]\frac{8}{142}\times 100[/tex]
[tex]\frac{800}{142}[/tex][tex]=5.63[/tex]
Therefore, the percentage error is 6% (approximately).
Therefore, the percent error in 1. is 20%
and the percent error in 2. is 6%
Composite figures are two or more figures combined. When finding the surface area, you cannot simply find the separate surface areas and add them. What face(s) do you have to exclude from the total surface area? Explain.
Step-by-step explanation:
You must exclude any intersecting faces (faces that are shared), because these faces are not on the surface.
For example, an ice cream cone can be approximated as a composite figure of a hemisphere on top of a cone. The circular base of the hemisphere and the circular base of the cone are intersecting, so you must exclude it when finding the surface area.
Answer:When two figures are placed together, one of each of their surfaces meets. The surfaces come together on the inside of the figure, and are no longer a part of the surface. These surfaces are a part of the individual figures’ surface area, but not of
Step-by-step explanation:
Did the test (this is the sample response)