Answer:
4 and 9
Step-by-step explanation:
let their ages be x and x - 5, then in 4 years their ages will be
x + 4 and x - 5 + 4 = x - 1 , and the product is 104, thus
(x + 4)(x - 1) = 104 ← expand factors on left using FOIL
x² + 3x - 4 = 104 ( subtract 104 from both sides )
x² + 3x - 108 = 0 ← in standard form
(x + 12)(x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 12 = 0 ⇒ x = - 12
x - 9 = 0 ⇒ x = 9
However, x > 0 ⇒ x = 9
Thus
Their present ages are 9 and 9 - 5 = 4
what is the rate for -6
Answer:A ratio is a comparison of two numbers or measurements. A rate is a special ratio in which the two terms are in different units. ... For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. The first term of the ratio is measured in cents; the second term in ounces.
Compare using >, <, or =
544 and 579
Answer:
579>544
Step-by-step explanation:
579 is greater than 544
Answer:
544<579
Step-by-step explanation:
544 is less than 579. This is because 544 is not more than 579. 579 is the bigger number . < means less than .> means greater than .= means equal to
i dont know how this is even considered college math lol.
60x60=1,200
What is wrong and how do we do it to find the answer.
(Explain and add and multiply)
Answer:
60 x 60 = 3600
Step-by-step explanation:
First if we wanted to, this is optionial, we can simplify this; 6 x 6 = 60 x 60
So 6x6 = 36, so for 60 x 60 we would add 2 0´s to the answer since we have 2 zeros added up in 60 and 60. so 60 x 60 = 3600
Rachel took clothes to the cleaners three times last month. First, she brought 3 shirts and 1 pair of slacks and paid $11.46. Then she brought 5 shirts, 2 pairs of slacks,
and 1 sports coat and paid $27.92. Finally, she brought 5 shirts and 1 sports coat and paid $19.94. How much was she charged for each shirt, each pair of slacks, and
each sports coat?
Rachel was charged for each shirt, $ for each pair of slacks, and $ for each sports coat.
Matrixes
Answer:
$2.49 each shirt$3.99 each slacks$7.49 each sports coatStep-by-step explanation:
If we let s, p, c represent the cost of cleaning the shirts, pants, and coats, respectively, the problem information lets us write three equations:
3s +1p +0c = 11.46
5s +2p +1c = 27.92
5s +0p +1c = 19.94
__
A variety of methods and tools are available for solving these equations. We can do it "by hand" using elimination and substitution.
Subtracting the 3rd equation from the 2nd, we get ...
(5s +2p +c) -(5s +c) = (27.92) -(19.94)
2p = 7.98
p = 7.98/2 = 3.99
Substituting this value into the first equation gives ...
3s +1(3.99) = 11.46
3s = 7.47 . . . . . . . . . . subtract 3.99
s = 7.47/3 = 2.49
Substituting this value into the last equation gives ...
5(2.49) +c = 19.94
c = 7.49 . . . . . . . . . . . subtract 12.45
Rachel was charged ...
$2.49 for each shirt
$3.99 for each pair of slacks
$7.49 for each sports coat
Answer:8.72 I think
Step-by-step explanation:
choose the mixed number that has not been reduced to simplest form.
7 14/18
4 2/5
5 7/12
5 5/6
A store sells 12 cans of soup for $7.50 How much would it cost to purchase 6 cans of soup?
Answer:
6 cans cost $3.75
Step-by-step explanation:
12 cans = $7.50 divided by 2 = $3.75
Answer:
6 cans cost 3.75
Step-by-step explanation:
7.50/2=3.75
Find three consecutive numbers whose sum is 84
Answer:
27,28,and29
Step-by-step explanation:
27+28+29=84
For example:
x+(x+1)+(x+2)=84
3x+3=84
3x=81
x=27
Now since x=27,replace the x
21+1=28
28+1=29
27+28+29=84
Hopes this helps :)
The three consecutive numbers whose sum is 84 is 27, 28 and 29.
Given the question to find three consecutive numbers whose sum is 84.
Consecutive numbers are numbers which lies next to each other in the set of counting numbers.
Let x be the starting number in the set of counting numbers.
Then the next consecutive number to it is x + 1.
And the next consecutive number to this is x + 2.
So we have,
x + x + 1 + x + 2 = 84
Adding like terms,
3x + 3 = 84
Subtracting 3 from both sides,
3x = 81
Dividing by 3 on both sides,
x = 27
So, x + 1 = 27 + 1 = 28
x + 2 = 27 + 2 = 29
Hence the numbers are 27, 28 and 29.
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15. True or False: Is x = 4 a solution to X + 51 = -9
True
False
The solution is Option B.
The value of x = 4 is not a solution to the equation | x + 5 | = -9
What is Modulus Function?
Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the equation be represented as A
Now , the value of A is
| x + 5 | = -9 be equation (1)
On simplifying the equation , we get
The modulus function always returns a positive value
So , when x = 4
Substitute the value of x = 4 in the equation , we get
| 4 + 5 | = -9
| 9 | = -9
And , 9 ≠ -9
Therefore , the equation is False
Hence , the solution is false and the modulus function returns a positive value
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Which of the following is equivalent to 36 -1.2
Answer:
34.8
Step-by-step explanation:
36-1.2 = 34.8
Find a linear equation whose graph is a straight line with the given properties through (0.5,6) and parallel to the line 4x-2y=15
Answer:
y = 2x + 5 or -2x + y = 5Step-by-step explanation:
Given line:
4x - 2y = 15Converted to slope-intercept form of y= mx + b
2y = 4x - 15y = 2x - 7.5Parallel lines have a same slope, so the line will be:
y = 2x + bUsing the point given (0.5, 6), finding the value of b:
y = 2x + b6 = 2*0.5 + bb = 6 - 1b = 5So the line is:
y = 2x + 5or
-2x + y = 5An item in a set is called a(n)
Answer:
An item in a set is called an element.
Step-by-step explanation:
I hope this helps.
2. A small square garden has an area of 25 square yards. How long is each side of
the garden?
O A. 2 yards
O B.2.5 yards
O
C. 5 yards
O D. 5.2 yards
The length of each side will be 5 yards. The correct option is C.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
Given that a small square garden has an area of 25 square yards. The side of the square will be calculated as,
The formula for the area of the square is,
Area = side²
25 = Side²
Side = √25
Side = 5 yards
Hence, the side of the square will be 5 yards.
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For each value of y, determine whether it is a solution to 12 = 2y +8.
Is it a solution
Answer: 2(0) + 8 does not equal 12, not a solution.
2(2) +8 = 12 yes it is a solution
2(-3) + 8 does not equal 12, not a solution
2(5) + 8 does not equal 12, not a solution.
Step-by-step explanation:
Looks like you need to plug in each y value given and multiplied by 2 and add 8
2(0) + 8 does not equal 12, not a solution.
2(2) +8 = 12 yes it is a solution
2(-3) + 8 does not equal 12, not a solution
2(5) + 8 does not equal 12, not a solution.
Identify equations from visual models (hanger
The hanger image below represents a balanced equation.
р
p
р
Write an equation to represent the image.
Answer: 3p=1/2
Just do it right now
find the next three terms in the pattern 4, 2, 0, -2, -4, ....... and complete the description of the pattern.
________ to get the next term. The next terms are ___, ____, and ____.
Options
Add 2
Add 4
Subtract 2
Subtract 4
Line AB is a straight line.
Pls use Statement & Reason
1. m∠AOB = ____________ 1. _________________________
2. m∠AOE+m∠EOF+m∠FOB=m∠_______ 2. _________________________
3. x + _________ +20° = _________ 3. Substitution
4. x = _________ 4. Algebra
Pls ANSWER FAST!!
Answer:
28°Step-by-step explanation:
Find the attachment in the diagram. According to the diagram, the sum of angle on the straight line AOB is 180°. Also the < AOD is equal to <COB (oppositely directed angle)
From the diagram;
m∠COE+m∠EOF+m∠FOB = <COB
Given
m<AOD = 152
m∠COE = 3x
m∠EOF = x
m∠FOB = x+ 12
Since < AOD = < COB, the expression above becomes;
m∠COE+m∠EOF+m∠FOB = m<AOD
Next is to substitute the given parameters into the formula above to get x;
3x+x+x+12 = 152
5x+12 = 152
subtract 12 from both sides of the equation
5x+12-12 = 152-12
5x = 140
divide both sides by 5;
5x/5 = 140/5
x = 28°
Hence the measure of angle x is 28°
I need help with this question
Answer:
i got w= 9/28 here is the equation i used because i couldn't tell what is said exactly: 6 2/3w= 15/7
Step-by-step explanation:
Answer:
i think its c
Step-by-step explanation:
Jordan is a teacher and takes home 40 papers to grade over the weekend. He can grade at a rate of 6 papers per hour. How many papers would Jordan have remaining to grade after working for 5 hours?
Answer:
10
Step-by-step explanation:
6x5=30
40-30=10
pls hepl very ugrent
Answer: x=12
Step-by-step explanation: x - 5 =12 the inverse operation of subtracting is adding so add 5 to both sides and you are left with x=7 + 5 the 5 on the left side cancels each other out so now all you do is add 5 to 7 and your left with x = 12
2.A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation 0.1. An item is considered to be defective if its weight is less than 9.8 pounds or greater than 10.2 pounds. Suppose that these items are currently produced in batches of 1000 units. a.Find the probability that at most 5% of the items in a given batch will be defective b.Find the probability that at least 85% of these items in a given batch will be acceptable.
Answer:
Step-by-step explanation:
Given that:
population mean = 10
standard deviation = 0.1
sample mean = 9.8 < x > 10.2
The z score can be computed as:
[tex]z = \dfrac{\bar x - \mu}{\sigma}[/tex]
if x > 10.2
[tex]z = \dfrac{10.2- 10}{0.1}[/tex]
[tex]z = \dfrac{0.2}{0.1}[/tex]
z = 2
If x < 9.8
[tex]z = \dfrac{9.8- 10}{0.1}[/tex]
[tex]z = \dfrac{-0.2}{0.1}[/tex]
z = -2
The p-value = P (z ≤ 2) + P (z ≥ 2)
The p-value = P (z ≤ 2) + ( 1 - P (z ≥ 2)
p-value = 0.022750 +(1 - 0.97725)
p-value = 0.022750 + 0.022750
p-value = 0.0455
Therefore; the probability of defectives = 4.55%
the probability of acceptable = 1 - the probability of defectives
the probability of acceptable = 1 - 0.0455
the probability of acceptable = 0.9545
the probability of acceptable = 95.45%
4.55% are defective or 95.45% is acceptable.
sampling distribution of proportions:
sample size n=1000
p = 0.0455
The z - score for this distribution at most 5% of the items is;
[tex]z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}[/tex]
[tex]z = \dfrac{0.0045}{\sqrt{\dfrac{0.04342975}{1000}}}[/tex]
[tex]z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}[/tex]
z = 0.6828
The p-value = P(z ≤ 0.6828)
From the z tables
p-value = 0.7526
Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526
The z - score for this distribution for at least 85% of the items is;
[tex]z = \dfrac{0.85 - 0.9545}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}[/tex]
[tex]z = \dfrac{-0.1045}{\sqrt{\dfrac{0.04342975}{1000}}}[/tex]
z = −15.86
p-value = P(z ≥ -15.86)
p-value = 1 - P(z < -15.86)
p-value = 1 - 0
p-value = 1
Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1
a. 0.7526
b. 1
Given that:
[tex]\sigma = 0.1\\\mu = 10\\[/tex]
It is given that item is acceptable if 9.8 < X < 10.2
Calculating standard variate value for :
1. x = 9.8:
[tex]z = \dfrac{x - \mu}{\sigma}\\[/tex]
z = -2
2. x= 10.2
[tex]z = \dfrac{x - \mu}{\sigma}\\[/tex]
z = 2
Now we can convert P( 9.8 < X < 10.2) to P(-2 < Z < 2).
Calculating
P(-2 < Z < 2) = P(Z <2) - P(Z < - 2)
= 0.9772 - 0.0227 (refer these values from z score table)
= 0.9545
Thus, the probability that an item from that population if randomly selected, it has 0.9545 probability to be acceptable.
And thus probability of an item to be defective is 1 - 0.9545 = 0.0455.
The batch size is 1000 unit.
The probability that at most 5% items are defective is calculated by z scores:
[tex]z = \dfrac{0.05-0.045}{\sqrt[2]{\dfrac{0.0455\times 0.9545}{1000}}}[/tex]
or
z = 0.6828
P( at most 5% defective) = [tex]P(Z \leq 0.6828)[/tex]
= 0.7526 ( from z score table).
[tex]z = \dfrac{0.85-0.9545}{\sqrt[2]{\dfrac{0.0455\times 0.9545}{1000}}}[/tex]
or
z = -15.8
and thus
P( at least 85% acceptable ) = P(Z >= -15.8) = 1- P(Z < -15.8)
P( at least 85% acceptable ) = 1 - 0 = 1
The z score tables give p values.
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Evaluate the expression. 5(x-2y)/2x+y when x=4 and y=-3
Answer:
10
Step-by-step explanation:
Step 1- Substitute the expression.
[tex]\frac{5(4-2(-3))}{2(4)+(-3)}[/tex]
Step 2- Multiply to simplify.
[tex]\frac{5(4+6)}{8-3}[/tex]
Step 3- Simplify the parenthesis.
[tex]\frac{5*10}{8-3}[/tex]
Step 4- Subtract.
[tex]\frac{5*10}{5}[/tex]
Step 5- Reduce the fraction with 5.
[tex]\frac{5*10}{5}[/tex] The 5's are crossed out when simplified.
= 10
f(x) = 2x - 3 for f(0).
What's a way to define absolute value
Find an expression which represents the difference when
Answer:
[tex]( - 2x + 2) - ( - 7x - 4)[/tex]
[tex] = - 2x + 2 + 7x + 4[/tex]
[tex] = - 2x + 7x + 2 + 4[/tex]
[tex] = 5x + 6[/tex]
hope it helped you:D
Jack use the place value chart below to show 1,826.5. Jack divided 1,826.5 by a number to get a quotient of 18.265 which he wrote on the second line of the chart. What number did Jack divide 1,826.5 by to get a quotient of 18,265?
Answer:
100Step-by-step explanation:
Let the number we are looking for be x. If Jack divided 1,826.5 by the number to get a quotient of 18.265, to get the number we will solve the equation;
1,826.5/x = 18.265
Cross multiply
1826.5 = 18.265x
Divide both sides by 18.265
18.265x = 1826.5
18.265x/18.625 = 1826.5/18.625
x = 100
Hence Jack divide 1,826.5 by 100 to get a quotient of 18.265
Here, we are required to find the number Jack divide 1,826.5 by to get a quotient of 18,265?
The number is 100
First, it is important to form an expression from the data given;
Let the no. which Jack divided 1,826.5 by be x.
The result of the division yields a quotient of 18.265.
From the statements above;
1,826.5/x = 18.265
Therefore, 1826.5 = 18.265x.
Therefore, x = 1826.5/18.265 = 100.
Therefore,
the number which Jack divided 1,826.5 by to get a quotient of 18.265 is x = 100.
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A rectangular garden is fenced on all sides with 258 feet of fencing. The garden is 7 feet
longer than it is wide. Find the length and width of the garden.
(w + 7) feet
w feet
The length of the garden is
feet.
The width of the garden is
feet.
Answer:
L = w + 8
P = 2L + 2w
256 = 2 (ancho + 8) + 2w
256 = 2 vías + 16 + 2 vías
256 = 4 semanas + 16
240 = 4w
w = 60
La longitud es 60 + 8 = 68
el ancho es 60
A number and its opposite is called
Answer: its called a additive inverse
Step-by-step explanation:
Answer:
the opposite positive number is negative, and the opposite to a negative number is positive.
Step-by-step explanation:
In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite number, sign change, and negation. For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive.
James mixes 7 cups of water with 2 scoops of lemonade mix. Charlie needs
to create a much larger batch of lemonade, so he mixes 25 cups of water with
10 scoops of mix.
Whose lemonade is stronger? Explain your reasoning,
The correct answer is Charlie's lemonade
Explanation:
The quantity of lemon vs sugar depends on the ratio each boy used. In the case of James, the ratio of water to the lemonade mix was 7:2. This means he 2 added scoops of lemonade for every 7 cups of water. On the other hand, the ratio of Charlie was 25: 10, which can be simplified as 5: 2 by dividing both numbers by a common divisor (5). This shows, Charlie's lemonade is stronger because he added the same lemonade mix in a lower amount of water, which would make the lemonade have a stronger flavor.
Is this answer right that I choose?
Answer:
your answer is incorrect thr correct answer is a
550 + 0.05c
Step-by-step explanation:
you are supposed to multiply 1/3 and 1650 then 1/3 * 0.15c
The variables x and y are related proportionally. When x = 8, y = 14. Find y when x = 36.
Answer:
y = 63 when x = 36
Step-by-step explanation:
The answer is 63 because 36 divide by 8 is 4.5 and 14 times 4.5 equals 63
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