The compound inequality expression expressing the required score to obtain a B grade is 80 ≤ (169 + t) ≤ 89
Test scores :
78 and 91Range of B - grade:
80 - 89Let the her score in the last test = t
Final average score will be :
(78 + 91 + t) / 3 = (169+t) / 3To obtain a B grade :
80 ≤ Final average score Final average score ≤ 89The compound inequality expression can be expressed thus :
80 ≤ Final average score ≤ 89Therefore, the compound inequality expression is 80 ≤ (169 + t) ≤ 89
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James buys a shirt and a pair of socks on sale for 25% off. if the price of the shirt before the sale was $24 and he spent a total of $24, what was the original price of the socks?
Answer:
The original price of socks was $8.
Step-by-step explanation:
James buys a shirt and a pair of socks on sale for 25% off.
The price of the shirt before the sale was $24 that means after discount the price was:
[tex]24-(0.25\times24)[/tex] = $18
And James paid a total of $24.
That means the price of socks after discount is = [tex]24-18[/tex] = $6
Let the original price of socks be x. And after 25% discount, it was for $6.
So, [tex]x-0.25x=6[/tex]
=> [tex]0.75x=6[/tex]
x = 8.
Hence, the original price of socks was $8.
A grocery store gives away a $10 gift card to every 25th customer and a $20 gift card to every 60th customer. a. Which customer will be the first to receive both gift cards?After this customer receives both gift cards, what is the total amount in gift cards that the store has given away?
What is the missing polynomial? ? – (20 – 4x – 5x2) = 20 – 7x2 A. 4x-12x^2 B. 4x-2x^2 C. 40-4x-12x^2 D. 40-4x-2x^2
A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t² + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.
Answer:
22 secs.
Step-by-step explanation:
h(t) = -16t^2 + 704t
The maximum will happen where the first derivative is equal to 0.
h’(t) = -32t + 704
-32t + 704 = 0 => -32t = -704 After subtracting 704 from both sides of the equation
Now divide both sides of the equation by -32
t = 22 secs.
Double Check: recalculated/reasonable ✅ ✅
Answer: 22 secs.
Just an interesting aside. After 22 secs, the projectile will be -16(22)^2 + 704(22) = -7744 + 15,488 = 7744 units up as its maximum height.
If it costs a restaurant $11.90 to produce 2 white chocolate tortes and each torte is cut into 8 slices, how much does each slice cost to make?
Final answer:
To find the cost of each slice of white chocolate torte, divide the total cost to produce two tortes ($11.90) by the total number of slices (16), resulting in approximately 74 cents per slice.
Explanation:
Cost of Each Slice of White Chocolate Torte
To calculate the cost of each slice of white chocolate torte, we start by determining the total cost of producing the tortes. The restaurant's cost is $11.90 for 2 tortes, and each torte is cut into 8 slices. This means there's a total of 2 tortes × 8 slices/torte = 16 slices. Dividing the total cost by the number of slices gives us the cost per slice:
Total cost for 2 tortes: $11.90
Number of slices per torte: 8
Total number of slices: 2 tortes × 8 slices/torte = 16 slices
Cost per slice: $11.90 / 16 slices = $0.74375 per slice
Therefore, each slice costs approximately 74 cents to make.
Which expression is equal to (3x−5)(2x−7)?
6x2−31x+35
5x2−21x+12
6x2+31x−35
6x2−31x−12
Answer:
[tex]6x^2-31x+35[/tex]
Step-by-step explanation:
Given expression,
[tex](3x-5)(2x-7)[/tex]
By using distributive property,
[tex](3x-5)(2x) - (3x - 5)(7)[/tex]
Again by distributive property,
[tex]3x(2x) - 5(2x) - 3x(7) + 5(7)[/tex]
[tex]6x^2 - 10x - 21x + 35[/tex]
[tex]6x^2-31x+35[/tex]
Hence, FIRST option is correct.
A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?
Answer:
Volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
Step-by-step explanation:
Formula to find the volume of a cone is V = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here r is the radius of the cone and h is the height of the cone.
Since radius of cone = [tex]\frac{1}{2}(\text{Radius of cylinder})[/tex]
= [tex]\frac{r}{2}[/tex]
Height of the cone = radius of the cylinder = r
Now we put the values of radius and height of cone in the formula
Volume of cone = [tex]\frac{1}{3}\pi (\frac{r}{2})^{2}(r)[/tex]
= [tex]\frac{1}{3}\pi(\frac{r^{2}}{4})(r)[/tex]
= [tex]\frac{1}{12}\pi r^{3}[/tex]
Therefore, volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]
What is the value of the underlined digit in the following number?
3.69
9 hundredths
90 hundredths
9 tenths
9 thousandths
.The population in the Northeast was 53,594,378 people in 2000 and 55,317,240 people in 2010. By about what percent did the population change? Did the population grow or shrink? Answer:
Which graph represents the function y – 3 = (x – 4)?
The graph represents the function y = (x - 1), as per linear equation.
What is a linear equation?A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.
The given equation is:
y - 3 = x - 4
⇒ y = x - 1
Therefore, for x = 0, y = - 1
for x = 1, y = 0
for x = - 1, y = - 2
Therefore, the graph will pass through points (0, - 1), (1, 0), (- 1, - 2).
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Answer:
its A
Step-by-step explanation:
Trevor is holding 5 red balloons and 4 blue balloons. He randomly selects a balloon to give his sister, and then he randomly selects a balloon to give his brother. Are two events dependent or independent? Explain.
A) Dependent. The two siblings will want the same color balloon.
B) Independent. Girls always want red and boys always want blue.
C) Independent. There are a set number of red balloons and blue balloons.
D) Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.
Answer:
Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.
Step-by-step explanation:
Whatever color the sister choses is irrelevant, eliminating answers A and B, but it does change the odds. If there are 5 red balloons and 4 blue balloons, if the sister is given a blue balloon, the odds of the brother receiving a red balloon increases (vis versa).
what are the real roots of 2x^3-42x-40
–2x + 3y = 21
3x – 2y = 21
–2x – 3y = 21
–2x + 3y = 7
Answer:
D.
Step-by-step explanation:
-2x+3y=7.I just took the test.
Figure ABCD is a parallelogram
Answer:
x = 7
Step-by-step explanation:
Figure ABCD is a parallelogram
So sides AD and BC will be parallel and their length will be same.
[Since opposite sides of parallelogram are equal in length]
So mAD = mBC
(5x + 3) = 38
5x = 38 - 3 = 35
x = [tex]\frac{35}{5}[/tex]
x = 7
Therefore, x = 7 will be the answer.
99 subtracted from m is 299. What is the equation for the sentence shown?
The expression of the word problem can be written as M-99=299 where M is 398.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 99 subtracted from m is 299. The expression for the word problem can be written as:-
M-99=299
M = 299 + 99
M = 398
Therefore, the expression of the word problem can be written as M-99=299 where M is 398.
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a jeweler bought some necklaces and bracelets for $1,100. the cost of the necklaces was 20% more than the cost of the bracelets. how much did the jeweler pay for
A) the necklaces?
B) the bracelets?
can 0.525252 be written as a fraction why or why not
What is the value of e^Ln7x ?
A. 1
B. 7e
C. 7x
D. 7
Answer:
the answer is 7x on edg... i just took the pretest
Step-by-step explanation:
For a party, liam ordered 1 taco for each guest, for $2.50 each, and paid a $2.00 delivery fee. michelle ordered 1 burrito for each guest, for $1.80 each, and paid a $3.00 delivery fee. let g represent the number of guests that attended the party. which simplified expression represents the total cost of the two orders?
a. 4.3g + 5
b. 4.5g + 4.8g
c. 6.3g + 3
d. 9.3g
Which statement could describe the dog’s movement 5 seconds after the command was given
Answer:
The dog is rather running towards the trainer to receive a treat. So it is the second answer.
Carrie made a square tablecloth with an area of 169 square inches. What was the length of each side of the tablecloth?
Plz hurry
The length of each side of the tablecloth is 13 inches.
Explanation:To find the length of each side of the tablecloth, we need to take the square root of the area. Since the area is given as 169 square inches, we can take the square root of 169. The square root of 169 is 13, so each side of the tablecloth is 13 inches long.
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Rewrite the given equation in slope intercept form:
5 y = 10 – 2 x
y = - 0.4 x + 2
Since the two lines are parallel, therefore they have similar slope which is – 0.4, so the equation is:
y = - 0.4 x + b
Given that x = 5, y = -4, find for b:
-4 = - 0.4 (5) + b
b = -2
So the answer is:
y = - 0.4 x – 2
or
2 x + 5 y = - 10
Find the interest for each loan. $252 at 8% for 2 years: ________ $400 at 2% for 6 months:________ $5,000 at 3.5% for 1 year:___________ $6,240 at 10% for 9 months: ___________
The interest for each loan is $40.32, $4, $175 and $468 respectively.
What is the formula to find the simple interest?The formula to find the simple interest is S.I=P×T×R/100.
Where, P=Principal, T=Time period and R=Rate of interest.
With P=$252, T=2 years and R=8%.
Now, SP=252×2×8/100=$40.32
With P=$400, T=6 months (0.5 years) and R=2%.
Now, SP=400×0.5×2/100=$4
With P=$5000, T=1 year and R=3.5%.
Now, SP=5000×1×3.5/100=$175
With P=$6,240, T=9 months (0.75 years) and R=10%.
Now, SP=6,240×0.75×10/100=$468
Therefore, the interest for each loan is $40.32, $4, $175 and $468 respectively.
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Veronica gave 20% of her money to Bill. She used 50% of the remaining money to buy books.
If Veronica gave $35 to Bill, she spent $ to buy books and she has $ left.
Answer:
If Veronica gave $35 to Bill, she spent $70 to buy books and she has $70 left.
Step-by-step explanation:
6L127ml=__________ mL
plz tell me what 3ab-9ab+7ab
The value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].
Further explanation:
There are two properties.
1. The property of addition or property of sum.
2. The property of subtraction.
3. The property of division.
4. The property of multiplication.
Given:
The equation is 3ab - 9ab + 7ab.
Explanation:
Consider the equation S = 3ab - 9ab + 7ab.
The equation contains the two variables that are “a” and “b”.
In the equation we have two operations one is addition and another is subtraction.
Solve the above equation to obtain the value of the equation.
First add 3ab and 7ab.
[tex]\begin{aligned}X&=3ab+7ab\\&=10ab\\\end{aligned}[/tex]
Now subtract 9ab from 10ab.
[tex]\begin{aligned}S&=10ab-9ab\\&=1ab\\&=ab\\\end{aligned}[/tex]
The value of S is ab.
Hence, the value of the equation 3ab - 9ab + 7ab is [tex]\boxed{ab}[/tex].
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Number System
Keywords: property, zero, eight, sum, addition, identity, shows, subtraction, number sentence, division, multiplication, variables.
what is the perimeter of a square with a side length of 5/7 units.
Irvan bought a drink for $1.90, a sandwich for $ 2.25, and an apple for $.75. What is the total amount of money he spent
Express 112 as a product of prime numbers in index form?
Final answer:
To express 112 as a product of prime numbers in index form, we perform prime factorization to get 2⁴ x 7.
Explanation:
To express 112 as a product of prime numbers in index form, we start by performing prime factorization, which is breaking down a composite number into the prime numbers that, when multiplied together, give the original number.
Let's find the prime factors of 112:
112 is divisible by 2 (the smallest prime number).112 ÷ 2 = 5656 is also divisible by 2, so 56 ÷ 2 = 28Continuing this process, 28 ÷ 2 = 14, and then 14 ÷ 2 = 7The number 7 is a prime number and cannot be divided further.So, we can express 112 as a product of prime factors as 2⁴ × 7¹ or simply 2⁴ × 7, since any number to the power of 1 is the number itself.
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Write the converse, inverse, and contrapositive for the following conditional statement. Determine whether the contrapositive is true or false and give reason why it is true or false.
Conditional Statement: If two segments are congruent, then they have the same length.
1.) Converse:
2.) Inverse:
3.) Contrapositive:
4.) Determine if the conditional statement below is TRUE OF FALSE. If False, provide a counterexample?
Conditional Statement:
If m∠A is greater than an acute ∠B, then ∠A must be obtuse.
The converse, inverse, and contrapositive of the given statement are provided. They are logically consistent with the original statement, pointing to the synonymous relationship between congruence and identical length in segments. The additional statement about angles is also factual, as one greater than an acute angle is, by definition, an obtuse.
Explanation:1.) Converse: If two segments have the same length, then they are congruent.
2.) Inverse: If two segments are not congruent, then they do not have the same length.
3.) Contrapositive: If two segments do not have the same length, then they are not congruent.
The contrapositive is true because it is a logical inverse of the original statement, which is also true. In geometry, congruent means being of the same size and shape, which directly implies having the same length.
4.) The statement: 'If m∠A is greater than an acute ∠B, then ∠A must be obtuse' is true. An acute angle is one that is less than 90 degrees. If ∠A is greater than this, it must be between 91 and 180 degrees, which by definition, makes it an obtuse angle.
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