what is the value of x?
Answer:
The answer is 5
A class of 25 students took a math test. Ten students had an average of 88. The other students had an average of 76. What is the average of the whole class?
A) 78.2
B) 80.8
C) 81.7
D) 82.5
The answer is B. 80.8
Answer:
The average of the whole class is 80.8.
The correct answer is B)
Step-by-step explanation:
To solve this problem, it is very important to understand the phrase: "Ten students had an average of 88". Let's see an example.
Imagine that three students in the class took a test and their scores were: 80, 89 and 95. To calculate the average of they three we must divide the sum of the scores by the total number of scores.
[tex]average=\frac{80+89+95}{3}=\frac{264}{3}=88[/tex]
The previous value is the average of the three students. Now, if we say that each student got 88, the average would be 88.
[tex]average=\frac{88+88+88}{3}=\frac{264}{3}=88[/tex]
The previous expression could be simplified as:
[tex]average=\frac{88\times 3}{3}[/tex]
Where, the number 3 means the number of students.
With that in mind, the phrase "Ten students had an average of 88" could be written as:
[tex]average_{10\, \, students}=\frac{88+88+88+88+88+88+88+88+88+88}{10}[/tex]
[tex]average_{10\, \, students}=\frac{88\times 10}{10}=88[/tex]
On the other hand, the phrase "The other students had an average of 76" means that from the 25 students, 15 students got 76 (25 - 10 = 15), and could be written as:
[tex]average_{15\, \, students}=\frac{76+76+76+76+76+76+76+76+76+76+76+76+76+76+76}{15}[/tex]
[tex]average_{15\, \, students}=\frac{76\times 15}{15}=76[/tex]
Finally, to calculate the total average of the 25 students we must divide the sum of the scores of all students by the total number of scores. The sum would be: 88+88+88+88+88+88+88+88+88+88+76+76+76+76+76+76+76+76+76+76+76+76+76+76+76, which equals [tex]88\times 10+76\times 15[/tex]. The total number of scores would be: 25.
[tex]average_{total}=\frac{88\times 10 + 76\times 15}{25}[/tex]
[tex]average_{total}=\frac{880 + 1140}{25}[/tex]
[tex]average_{total}=\frac{880 + 1140}{25}[/tex]
[tex]average_{total}=\frac{2020}{25}[/tex]
[tex]average_{total}=80.8[/tex]
Thus, the average of the whole class is 80.8. The correct answer is B)
HELPPPP WILL GIVE BRAINLIEST
Answer:
79
Step-by-step explanation:
Since the triangles are similar, the sides that are the same length have angles that are the same size at the top.
A can has a radius of 2 inches and a volume of 62.8 cubic inches. Find the height of the can.
The formula for the volume of a cylinder is V=\pi r^2h V = π r 2 h . Rewrite this formula to solve for h.
Use your formula to find the height, h, of the can. Use 3.14 for \pi π .
By rearranging the formula for the volume of a cylinder to solve for height, and substituting the given values for volume and radius, we find that the height of the can is 5 inches.
To solve for the height h of the cylinder, we need to rearrange the formula for the volume of a cylinder, V =
2h, to solve for h. This is done by dividing both sides of the equation by
2, thus isolating h on one side of the equation.
The rearranged formula becomes:
h = V / (2)
Using the given volume of the can, 62.8 cubic inches, and the given radius of 2 inches, we plug these values into our formula:
h = 62.8 / (3.14 × 2²)
h = 62.8 / (3.14 × 4)
h = 62.8 / 12.56
h = 5 inches
Therefore, the height of the can is 5 inches.
Write the equation of the parabola in standard form that passes through the points (0, 3), (1, -4), and (-1, 4).
Answer
[tex]y = -3x^2-4x+3[/tex]
Explanation
The standard form of a parabola is
[tex]y = ax^2 + bx + c,[/tex]
where [tex]a \ne 0[/tex], and [tex]a,b,c[/tex] are real numbers.
If it passes through (0,3) then when x = 0, y = 3 so this means that
[tex]3 = a(0)^2 + b(0) + c \implies c = 3[/tex]
so [tex]y = ax^2 + bx + 3[/tex].
If it passes through (1,-4), then when x = 1, y = -4 so
[tex]\begin{aligned}-4 &= a(1)^2 + b(1) + 3 \\a+b+3 &= -4 \\a+b &= -7 && \text{(I).}\end{aligned}[/tex]
If it passes through (-1,4) then when x = -1, y = 4 so
[tex]\begin{aligned}4 &= a(-1)^2 + b(-1) + 3 \\a-b+3 &= 4 \\a-b &= 1 && \text{(II).}\end{aligned}[/tex]
Because both (I) and (II) need to be satisfied, we have the system of equations,
[tex]\begin{cases}a+b &= -7\qquad\text{(I)}\\a-b &= 1\qquad\text{(II)}\end{cases}[/tex]
which we can easily solve by adding the two equations up to get
[tex]\begin{aligned}(a+a) + (b-b) &= -7 + 1 \\ 2a&= -6 \\a &= -3.\end{aligned}[/tex]
Then we take any of the previous equations to solve for b:
[tex]\begin{aligned}a+b &= -7\\-3 + b &= -7 \\ b &= -4\end{aligned}[/tex]
Thus the parabola in standard form is
[tex]y = -3x^2-4x+3.[/tex]
So with the three points that are given to us, we will plug them into the standard form formula that I had mentioned earlier. Firstly, plug (0,3) into the equation since the 0 will cancel out the a and b variable:
[tex]3=a*0^2+b*0+c\\3=c[/tex]
Now we know that the value of c is 3.
Next, plug (1,-4) into the standard form formula and simplify (Remember to plug 3 into the c variable):
[tex]-4=a*1^2+1*b+3\\-4=a+b+3\\-7=a+b[/tex]
Next, plug (-1,4) into the standard form formula and simplify:
[tex]4=a*(-1)^2+b*(-1)+3\\4=a-b+3\\1=a-b[/tex]
With the last two simplified equations, we will create a system of equations:
[tex]-7=a+b\\1=a-b[/tex]
With this, I will be using the elimination method. Add the two equations together, and the following equation is the result:
[tex]-6=2a[/tex]
From here we can solve for a. For this, just divide both sides by 2:
[tex]-3=a[/tex]
Now that we have the value of a, plug it into either equation to solve for b:
[tex]-7=-3+b\\-4=b\\\\1=-3-b\\4=-b\\-4=b[/tex]
AnswerNow, plug the obtained values in our standard form equation and your final answer will be:
[tex]y=-3x^2-4x+3[/tex]
Solve the inequality below to determine and state the smallest possible value for x in he solution set 3(x+3)<5x-3
Seattle, wa and san francisco, ca lie on the same longitudinal line. san francisco is at 38° latitude and seattle is at 47° latitude. if the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [use π = 3.14, and round to the nearest mile.]
Step 1.
Calculate measure of angle α:
[tex]47^o-38^o=9^o[/tex]
Step 2.
Calculate what fraction of the angle 360° is the angle α:
[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]
Step 3.
Calculate the circumference of the Earth (circle):
[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]
Step 4.
The length of arc is equal 1/40 of the circumference:
[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]
[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]
The distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is approximately 628 miles, calculated using the formula for arc length of a sphere, considering the Earth's radius and the difference in degrees of latitude.
Explanation:The question revolves around the concept of calculating the arc length in degrees, which is a topic in mathematics, specifically trigonometry.
The formula for calculating the arc length of a sphere is arc length = radius x angle (in radians).
We already know the radius of the earth (4000 miles) and the difference in latitude between Seattle and San Francisco (47°-38°=9°).
However, in the formula, we need the angle to be in radians. To convert degrees to radians, we use the formula 1 degree = π/180 radians.
So, 9° equals 9*(π/180) = 0.157 radians.
Now, we substitute the values into the formula: arc length = 4000 miles * 0.157 radians. This gives an answer of approximately 628 miles.
Therefore, the distance between San Francisco, CA, and Seattle, WA, along the longitudinal line is about 628 miles.
Learn more about Arc Length here:https://brainly.com/question/32035879
#SPJ3
solve the inequality a-3 ≤-8
Answer:
a is less than or equal to -5
Step-by-step explanation:
Answer:
a ≤-5
Step-by-step explanation:
a-3 ≤-8
Add 3 to each side
a-3 +3≤-8+3
a ≤-5
PLEASE ANSWER ASAP
Which value of x makes the inequality 2(8 – x) < 4 true?
A. x = –16
B. x = –9
C. x = 4
D. x = 10
First, let's ignore the answer choices and solve for a value of x ourselves.
2(8 - x) < 4
Distributive property.
16 - 2x < 4
Subtract 16 from both sides.
-2x < -12
Divide both sides by -2 (and flip the inequality sign)
x > 6
The value of x is going to be greater than 6, and so, we can observe the answer choices, and whichever value is greater than 6, is the correct answer.
In this case, there is only one answer, and that is D, x = 10.Answer:
d x=10
Step-by-step explanation:
The sum of two numbers is 96. The difference of the same two numbers is 8. What is the larger number?
Answer:
The larger number is 52.
Step-by-step explanation:
To find this number, we have to create a statement for both of the equations that are given.
x + y = 96
x - y = 8
Now we can add them together to solve for x (which is the larger number).
x + y = 96
x - y = 8
-------------
2x = 104
x = 52
CAN SOMEONE PLEASE HELP ME I NEED TO KNOW THIS LIKE NOW ITS SUPER IMPORTANT
IF GIVEN A THEOREM, HOW DO YOU DETERMINE WHAT IS THE GIVEN INFORMATION AND WHAT IS THE TO PROVE INFORMATION
Answer:
the information is in the theorem itself and to prove it set up an equation in the same format the theorem uses and test it.
Step-by-step explanation:
PLEASE HELP!!
I can pay $4.50 for a 2-mile taxi ride or $8 for 7 miles ride. At this rate, how much would an 11-mile ride cost?
Slope intercept
Answer:
The answer is $10.80
Step-by-step explanation:
It goes up $0.70 every mile and the flat fee is $3.10.
The equation 3.1 + 0.7(x) when x is the number of miles traveled.
Substitute 11 for x and get 3.1 + 0.7(11).
The answer is $10.80
An elephant needs to drink at least 40 gallons of water each day. A drinking tank contains 4 gallons of water. The elephant has already consumed 24 gallons of water. How many tanks x of water does the elephant need to drink? Write your answer as an inequality.
The solution is____
{Will receive 15 pts.}
Please help!!
Answer:
4
Step-by-step explanation:
40-24=16
16/4=4
4 tanks
A company makes and sells charm bracelets. The cost of producing x bracelets is represented by the function. C(x)=180+8x. The revenue earned for selling x bracelets is represented by the function R(x)=20x. Write and simplify a function P the represents the profit made from selling x bracelets. How many must the company sell to break even
Answer:
Minimum 15 bracelets to be sold to meet the break even.
Step-by-step explanation:
The cost price of bracelets is represented by C(x) =180+8x
The revenue earned (selling price) is represented by R(x) =20x
In these two functions x represents number of bracelets.
If P represents the profit then P = 20x-(180+8x)
P = 20x-180-8x = (12x-180)
For break even profit P = 0
12x-180 =0
12x = 180
x = 180÷12
x = 15
So minimum quantity of bracelets to be sold is 15 for the break even.
Please answer these 4 questions asap! Thanks so much!
Answer:
A
B
Q
D
Step-by-step explanation:
The state of Colorado is shaped like a rectangle with an approximate width of 280 mi and length of 380 mi. What is the population density of Colorado in people per square mile if the population is 5,116,800?
Answer:
Step-by-step explanation:
160miles • 330miles= 52,800square miles
Now it wants the population density in people per square miles, so you need to divide the population by the number of square miles.
4779736/52800=90.5 which is about 91people per square mile.
The population density of Colorado is 48.09 people per mile²
Population densityPopulation density is the concentration of individuals within a specific area. It is given by:
Population density = number of people / land area
Land area = length * width = 280 * 380 = 106400 mile²
Population density = 5,116,800 / 106400 = 48.09 people per mile²
The population density of Colorado is 48.09 people per mile²
Find out more in Population density at: https://brainly.com/question/13902749
What is the largest number of identical goody bags that can be using 50 bouncy balls and 110 pokemon cards?
Answer:
10 goody bags.
Step-by-step explanation:
We are asked to find the largest number of identical goody bags that can be using 50 bouncy balls and 110 pokemon cards.
In order to solve our problem we will use GCF (Greatest common factor). Let us find out GCF of 50 and 110.
The factors of 50 are: 1, 2, 5, 10, 25, 50.
The factors of 110 are: 1, 2, 5, 10, 11, 22, 55, 110.
We can see that GCF of 50 and 110 is 10 as 10*11=110 and 10*5=50.
Therefore, the largest number of identical goody bags is 10 with 5 bouncy balls and 11 pokemon cards in each goody bag.
The Point located at open ( 3, –1 ) is reflected across the y-axis what are the coordinates of the reflected point
Answer:
(-3, -1)
Step-by-step explanation:
As its reflected across the y-axis the y coordinate remains the same but the new x-coordinate is the opposite value.
Which compound sentence has its solution set shown on the graph below?
2x - 4 > 6 or 3x < 9
2x - 4 < 6 and 3x > 9
3x + 8 > -7 or -4x < 12
3x + 8 < -7 and -4x > 12
There might be a simpler way to do this, if there is, sorry.
If you look at the graph, x is greater than 3 but less than 5.
So: x > 3 and x < 5
I would simplify each solution set and get "x" by itself (until I get the right answer):
A.) 2x - 4 > 6 or 3x < 9
2x - 4 > 6 Add 4 on both sides
2x > 10 Divide 2 on both sides
x > 5 (you could stop here and go to the next choice since you know this does not match the graph)
3x < 9 Divide 3 on both sides
x < 3
x > 5 and x < 3
B.) 2x - 4 < 6 and 3x > 9
x < 5 and x > 3
Your answer is B or the 2nd option
[C and D would have given a negative number]
The compound sentence that has its solution set shown on the graph is 3x + 8 > -7 and -4x < 12.
The solution set for the given compound inequalities is represented by the graph where the shaded region includes the points -1, 0, 1, 2, 3, 4, and 5. The compound sentence that has this solution set is:
3x + 8 > -7 and -4x < 12
Let's break down the compound sentence step by step:
Solve the first inequality: 3x + 8 > -7. Subtract 8 from both sides to get 3x > -15. Divide both sides by 3 to get x > -5.
Solve the second inequality: -4x < 12. Divide both sides by -4 and flip the inequality sign to get x > -3.
Combine the two inequalities by using the word 'and': x > -5 and x > -3.
The solution to this compound sentence is the values of x that satisfy both inequalities, which is x > -3.
Therefore, the compound sentence 3x + 8 > -7 and -4x < 12 has its solution set shown on the given graph.
Learn more about Compound here:
https://brainly.com/question/31904612
#SPJ2
A furniture maker is building a bookshelf. He needs to cut rectangular pieces of wood to a length of 5/12 foot and a width of 2/3 foot.What is the area of a piece of wood that size?
Answer:
[tex]\frac{5}{18}[/tex] square feet.
Step-by-step explanation:
We have been given that the length of a rectangular piece of wood is 5/12 foot and width is 2/3 foot.
Since area of a rectangle is width times length, so to find the area of piece of wood we will multiply 5/12 by 2/3.
[tex]\text{Area of wood}=\frac{5}{12}\times \frac{2}{3}[/tex]
[tex]\text{Area of wood}=\frac{5}{6}\times \frac{1}{3}[/tex]
[tex]\text{Area of wood}=\frac{5}{6\times 3}[/tex]
[tex]\text{Area of wood}=\frac{5}{18}[/tex]
Therefore, area of piece of wood will be [tex]\frac{5}{18}[/tex] square feet.
A community hall is in the shape of a cuboid the hall is 40m long 15m high and 3m wide. 10 litre paint covers 25m squared costs ?10. 1m squared floor tiles costs ?3. Work out the total costs of tiles and paints
The total cost of painting and tiling a community hall shaped as a cuboid with the given dimensions is £972. This is based on calculating the surface area for paint and the floor area for tiles, then multiplying by the respective costs per m².
Explanation:To solve this problem, we first need to figure out the total surface area of the cuboid, which will include the floor area for the tiles, and all sides for the paint.
Surface area of the cuboid involves calculating area for all six sides, which totals to 2*(lb + bh + hl), where l is length, b is breadth, and h is height.
Substituting the values given, the total surface area of the cuboid is 2*(40*15 + 15*3 + 3*40) = 2*(600 + 45 + 120) = 2*765 = 1530m2.
The floor area is length * breadth i.e., 40m * 3m = 120 m2.
Next, we calculate the cost of painting and tiling. We know 10 liters of paint covers 25 m2 and costs £10.
So, 1 litre covers 25/10 = 2.5m2 and similarly costs £10/10 = £1.
Therefore, the paint costs for 1530 m2 are 1530/2.5 = 612 litres * £1/litre = £612.
For tiling, the cost for 1m2 is £3, so for a 120 m2 floor, the cost will be 120m2*£3/m2 = £360.
Therefore, the total cost for paint and tiles is £612 + £360 = £972.
https://brainly.com/question/30694298
#SPJ12
I need a problem with 1/3 + 1/8. Something like "Jasmine buys 1/2 of apples but Pedro takes 1/4, how many apples does Jasmine have now? 1/4 of apples" (please be something easy!Im from 5th year
An avocado tree has a sale price of $27.95 dollars; this is 65% off the original price. What percent of the original price was the discount and how much was deducted from the original price?
Answer:
35% off, deducts $15.05
Step-by-step explanation:
The sale price was $27.95 and is 65% of the original price. This means the sale was 100%-65%= 35% off the original price.
We can create a proportion to find the original price to see how much was deducted. A proportion is an equation where two ratios are set equal to each other. We create two fractions using the prices and percents.
[tex]\frac{27.95}{x} =\frac{65}{100}[/tex]
We begin solving by cross multiplying numerator to denominator of each fraction.
[tex]27.95(100)=65(x)\\2795=65x\\\frac{2795}{65}=\frac{65x}{65} \\43=x[/tex]
So the original price was $43. The sale price deducts 43-27.95= 15.05
if a normal distribution has a mean of 132 and a standard deviation of 20 what is the value that has a z score of 1.8?
Answer:
168 = x
Step-by-step explanation:
mean = u=132
standard deviation =sigma = 20
z score =z=1.8
The formula is
z = (x-u)/ sigma
Substituting what we know
1.8 = (x-132)/20
Multiply by 20
1.8*20 = (x-132)/20 *20
36 = x-132
Add 132 to each side
36+132 = x-132+132
168 = x
Multiply the standard deviation by the z-score and add that to the mean:
Value = 132 + (20*1.8) = 132 + 36 = 168
The value would be 168.
Your favorite baseball player is doing much better this year than he did last year. Last year he got 56 hits. This year he has 3 times as many hits. How many hits does he have this year?
Answer:168
Step-by-step explanation:
56 x 3 = 168
If a room is 16 1/2 feet by 18 1/2 feet in size and the carpet cost 17.50per square yard what is the total cost of the room
Find the value of 64 ÷ 2 · 16.
Answer:
512
Step-by-step explanation:
64 / 2 = 32
32 * 16 = 512
64 / 2 * 16 = 512
Please rate Brainliest (:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{62 \div 2 \times 16}\\\\\mathsf{= \dfrac{62}{2} \times 16}\\\\\mathsf{= \bold{32}\times16}\\\\\mathsf{= \bf 512}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{512}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the value of x.
Answer:
7 sqrt(3) =x
Step-by-step explanation:
We know that sin 60 = opposite / hypotenuse
sin 60 = x/14
Multiply both sides by 14
14 sin 60 = x
14 * (sqrt(3)/2) =x
7 sqrt(3) =x
The times for three runners in a 100-meter race are 9.85 s, 9.6 s and 9.625 s. What is the winning time?
ONLY THE BRAINLIEST OF USERS ANSWER THIS QUESTION 30 POINTS!!!!!!!!!!!!!!!
Give the function that defines the given sequence.
-8,-20,-50,-125,-625/2
PLEASE NEED HELP NOW
Answer:
8*5^n-1 / 2^n-1 = n
This is the function for your sequence
8*5^n-1 / 2^n-1 = n
The Sequence Calculator finds a equation of the sequence or also allows you to view the next terms in a sequence. Arithmetic Sequence Formula: an = a1 +d(n −1) a n = a 1 + d (n - 1) Geometric Sequence Formula: an = a1rn−1 a n = a 1 r n - 1
What does the word function mean in math?f (3) f ( 3) and g(3) g ( 3)f (−10) f ( − 10) and g(−10) g ( − 10)f (0) f ( 0)f (t) f ( t)f (t +1) f ( t + 1) and f (x +1) f ( x + 1)f (x3) f ( x 3)g(x2−5) g ( x 2 − 5)How do you find the Fraction form in math?Divide the numerator by denominatorWrite down the whole number resultUse the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.Learn more about function here https://brainly.com/question/12431044
#SPJ2