Answer:
25 t-shirts and 35 hats were sold
Step-by-step explanation:
Here, we want to calculate the number of hats and the number of t-shirts sold.
Let the number of hats be h and the number of t-shirts be t
The sum of both is 60;
Mathematically;
h + t = 60 •••••••••••(i)
The total revenue from selling h hats at $12 per one is 12 * h = $12h
The total revenue from selling t t-shirts at $18 per one is 18 * t = $18t
So the addition of this gives the total;
12h + 18t = 870 ••••••••(ii)
From i, h = 60-t; substitute this into ii
12(60-t) + 18t = 870
720 -12t + 18t = 870
720 + 6t = 870
6t = 870 -720
6t = 150
t = 150/6
t = 25
From the substitution;
h = 60-t
h = 60-25
h = 35
Answer:
48 hats
Step-by-step explanation:
im not sure if this is the right answer but i hope this helps
If you deposit $200 into a CD (Certificate of Deposit) with an interest rate of 1% for 3 years, how much simple interest will you earn after
THREE years?
O $1
$5
$6
$25
Answer:
$6
Step-by-step explanation:
A=P(1+i.n)
A=200(1+0.01.x 3)
A=206
Thus 206 - 200 = $6
You will earn $6 in interest.
The interest you will earn per year is:
= Interest rate x Amount deposited
= 200 x 1%
= $2
Because it is simple interest, you will earn the same amount of interest every year. In 3 years you will have:
= Interest per year x number of years
= 2 x 3
= $6
You will therefore earn $6 in interest.
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Rectangle with width labeled on the right, width equals 4 and 1 over 2 inches. Below the rectangle, it says, length equals question mark. Inside the rectangle, it says area equals 36 and 3 over 4 square inches.
Answer:
length = [tex]8\frac{1}{6}[/tex] inches
Step-by-step explanation:
A rectangle is a quadrilateral which has opposite sides to be equal.
Area of a rectangle = length × width
Given that: Area = [tex]36\frac{3}{4}[/tex] square inches, width = [tex]4\frac{1}{2}[/tex] inches, length = l. Thus;
[tex]36\frac{3}{4}[/tex] = l × [tex]4\frac{1}{2}[/tex]
[tex]\frac{147}{4}[/tex] = l × [tex]\frac{9}{2}[/tex]
divide both sides by [tex]\frac{9}{2}[/tex],
l = [tex]\frac{147}{4}[/tex] ÷ [tex]\frac{9}{2}[/tex]
= [tex]\frac{147}{4}[/tex] x [tex]\frac{2}{9}[/tex]
= [tex]\frac{49}{6}[/tex]
l = [tex]8\frac{1}{6}[/tex]
Therefore, the length of the rectangle is [tex]8\frac{1}{6}[/tex] inches.
2
Lena tutors chemistry. For each hour that she tutors, she earns 30 dollars.
Let E be her earnings (in dollars) after tutoring for H hours.
E
Write an equation relating E to H. Then use this equation to find Lena's earnings after tutoring for 19 hours.
Equation:
x
5
?
Lena's earnings for 19 hours: I dollars
Answer:
[tex]E = 30 \times H[/tex]
$570
Step-by-step explanation:
Given that:
For each hour of tutoring, Lena earns 30 dollars.
E is her earning and
H is the number of hours for which she tutors.
To find:
Equation relating E to H.
Solution:
Let Lena tutors for 1 hour, then the earning = 30 dollars
Let Lena tutors for 2 hours, then the earning = 30+30 OR 2[tex]\times[/tex]30 = 60 dollars
Let Lena tutors for 3 hours, then the earning = 30+30 +30 OR 3[tex]\times[/tex]30 = 90 dollars
If Lena tutors for H number of hours, then the earning, E = 30 + 30 + .... + 30 (H times) i.e.
[tex]E = 30 \times H[/tex]
So, the equation that relates E to H is given as:
[tex]E = 30 \times H[/tex]
Now, it is given that she tutors for 19 hours.
Let us put H = 19 hours in the above equation:
[tex]E = 30 \times 19 \\\Rightarrow E = \$570[/tex]
Therefore, the earning for 19 hours of tutoring is 570 Dollars.
Emilio throws a marshmallow into the air from his balcony. The height of the marshmallow (in feet) is represented by the equation h=−16(t−14)2+49, where t is the time (in seconds) after he throws the marshmallow. What is the maximum height of the marshmallow? Enter your answer as the correct value, including units, like this: 42 meters Be sure to use the correct units from the context of the problem.
Answer:
49 ft
Step-by-step explanation:
h=−16(t−14)^2+49
The path of the marshmallow is an inverted parabola. It has symmetry with respect to its vertical axis.
We take the derivative of the height function.
dh/dt = -32(t - 14)
dh/dt = -32t + 448
We set the derivative equal to zero ti find the value of t corresponding to a maximum value of h.
-32t + 448 = 0
-32t = -448
t = 14
Maximum height occurs at t = 14 seconds.
h=−16(t−14)^2+49
t = 14
h=−16(14−14)^2+49
h = 49
Maximum height is 49 feet.
What is the value of x in the equation 32(4x – 1) – 3x = 54 – (x + 2)?
Answer:
Step-by-step explanation:
32(4x - 1) - 3x = 54 - (x+2) : Do 32 times 4 and -1 as well as -1 times x and 2
128x - 32 - 3x = 54 - x - 2 : Combine like terms
125x - 32 = 52 - x : Add x to both sides
126x - 32 = 52 : Add 32 to both sides
126x = 84 : Divide both sides by 126
x = 0.666666667 : Round to the tenth
x = 0.67 : Final answer
Is 1.8x10-4 greater than 7.2x10-1and how many times greater
Answer:
ye s1.8x10-4 is greater than 7.2x10-1
Step-by-step explanation:
The number 1.8*10⁻⁴ is smaller, not larger than 7.2*10⁻¹
Is the first number greater than the second?We have two numbers in scientific notation, these are:
1.8*10⁻⁴
7.2*10⁻¹
We want to see if the first one is larger than the second one. This is trivial to notices, because the exponent in the first number is 3 orders of magnitude smaller than the other exponent, then the first number is smaller than the second, not larger.
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Simplify the expression
8
2
+
9
(
12
÷
3
×
2
)
−
7
. Explain each of your steps.
Answer:
147
Step-by-step explanation:
82+9(12÷3×2)-7
82+9(4×2)-7
82+9(8)-7
82+72-7
154-7
147
Follow PEMDAS
The simplified values of the expression is 97.
How to apply BODMAS rule ?First we will solve what is inside the brackets that too in 1st 2nd and 3rd bracket order then we will divide after that we will multiply then we will add then subtract.
The given equation is
82 + 9 (12 ÷ 3×2) - 7
Here we will follow BODMAS rule
BODMAS stands for Brackets of order division multiplication addition and substraction. In this order we will solve our expression
82 + 9 (12 ÷ 3×2) - 7
= 82 + 9(12 ÷ 6) - 7
= 82 + 9(2) - 7
=82 + 18 - 7
=100 - 7
= 97
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Answer two questions about Equations A and B:
A. 5= -2(x - 1)
B. 5 = -22 + 2
1) How can we get Equation B from Equation A?
Choose 1 answer:
Answer:
part 2 is A: yes
Step-by-step explanation:
Option B is correct.
We have the two following equations -
A. 5 = -2(x - 1)
B. 5 = -2x + 2
We have to find out how can we get Equation B from Equation A?
State the distributive property.According to the distributive property -
a(y + z) = (a x y) + (a x z)
According to the question -
We have -
-5 = -2(x - 1)
Using the distributive property, we can rewrite the right hand side as follows -
-5 = -2(x - 1) = ( -2x ) + (2) = -2x + 2
Hence, option B is correct.
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2p+1÷5p+6 =1÷7 whats the answer
Answer:
The result can be shown in multiple forms.
Exact Form:
p= - 13/19
Decimal form:
p= - 0.68421052...
what is the area of the square length:10 width 15
Answer:
5 I think because don't you divide
Answer 150β
10 times 15
You want to surround the perimeter of a garden with 35 stones. You need to place a certain number of large and small stones, and for every large
stone, you want to use 4 small stones. Choose the correct equation to find the number of stones for each size. Then solve the equation
OAX + 4x = 35,7 large stones and 28 small stones
O B. X+5x = 35, 7 large stones and 28 small stones
O cx + 4 = 35, 4 large stones and 31 small stones
D. 4x = 35 + x 12 large stones and 23 small stones
Answer: A) x + 4x = 35; 7 large stones and 28 small stones
======================================================
Explanation:
x = number of large stones
4x = number of small stones
x+4x = total number of stones = 35
x+4x = 35 is the equation to solve
-----------
Let's isolate x
x+4x = 35
5x = 35
x = 35/5
x = 7 large stones are needed
4x = 4*7 = 28 small stones are needed
You have four quiz grades. Quiz 1: 17/30, Quiz 2: 17/25, Quiz 3: 38/50, Quiz 4: 18/25 What is your ordinary quiz average?
What is your weighted quiz average?
Answer:
.7 or 70%
Step-by-step explanation:
17/30 + 17/25 + 38/50 + 18/25 = 2.727
2.727 divided by 4 (the amount of addends) = .7
Answer:
68%
Step-by-step explanation:
To find the average quiz grade, you have to add up all the percentages and divide by the numbers of scores you have.
56 + 68 + 76 + 72 = 272
272 ÷ 4 = 68
Hope this helps! <3
The area is square feet of a rectangular garden can be expressed as the product of the garden's length and
width, or A(x) = 2x2 - 21x + 40. If the width of the garden is (x - 8) feet, what is the length of the garden?
Answer:
(2x-5)feet
Step-by-step explanation:
The area of the rectangular garden A = Length × Width
Given the area A(x) = 2x² - 21x + 40
And the width =x-8 feet
To get the length, we will simply factorise the area function as shown;
You will just factorise the area
Factorizing 2x² - 21x+40
2x² − 21x + 40
2x² -16x - 5x + 40
2x(x - 8) -5(x - 8)
=(2x−5)(x−8)
Hence the length of the garden is
(2x-5)feet
24x squared – 44x + 12
please help!!
Answer:
Using the quadratic formula:
x = [--44 +- sqr rt (-44^2 -4*24*12)] / 4*12
x = [44 +- sqr rt (1,936 -1,152)] / 48
x = [44 +- SQR RT (784)] / 48
x = (44 +- 28) / 48
x1 = 72 / 48 = 1.5
x2 = 16 / 48 = 1 / 3 = .3333333333...
Step-by-step explanation:
Convert 0.3185° to minutes and seconds
Answer:
Step-by-step explanation:
19 minutes and 16 seconds . because there are 60 minutes in every degree . and 60 seconds in every minute. so, if you take 0.3185 x 60 = 19.11 minutes . —-> 19.11 min. x 60 = 6.6 seconds .
so therefore the answer is 19 min. &’ 16 seconds ur welcome
Answer:
23 min 6 seg
Step-by-step explanation:
0,3185º =
0,3185*60 min = 23,1 min =
23 min + 1/10 de min
1/10 de min = 1/10 * 60 seg = 60/10 = 6 seg
Laura has a collection of coins that includes pennies, nickels, dimes, and quarters. The total amount of money she has in dollars can be found using the expression (P + 5N + 10D + 25Q) ÷ 100
Answer:
3.84
Step-by-step explanation:
((24) + 5(12) + 10(10) + 25(8)) ÷ 100 = (24 + 60 + 100 + 200) ÷ 100 Multiply.
= (384) ÷ 100 Add.
= 3.84 Divide.
pls someone, pls explain aswell !!
Answer:
absolute value
Step-by-step explanation:
What is the product written in scientific notation? (1.18×10^3)⋅(9.1×10^−6)
Answer:
1.0738 x 10^-2
Step-by-step explanation:
How can you represent patterns from everyday life by using tables, expressions, and graphs?
Answer:
"They organize data and can reveal relationships, making it easier to write equations that describe the patterns."
Step-by-step explanation:
A right triangle and its dimensions are shown in this diagram.
26 meters
10 meters
24 meters
What is the area, in square meters, of the triangle?
Answer: The answer is B
Step-by-step explanation:
What is the solution to the compound inequality 5x + 7 ≥ −8 and 3x + 7 < 19?
Answer:
x[tex]\geq[/tex]-3 and x<4
Step-by-step explanation:
5x[tex]\geq[/tex] -15 and 3x<12
x[tex]\geq[/tex] -3 and x<4
Now you just need to graph it :)
I need help understanding mean median
If 40% of any number is 600 more than its 25%. What is the number?
Answer:
4000
Step-by-step explanation:
40% of the number is 15% more of the number than 15% of the number is. So, 600 is 15% of the number.
600 = 0.15n
600/0.15 = n = 4000
The number is 4000.
__
Check
40% of 4000 is 1600. 25% of 4000 is 1000. 1600 is 600 more than 1000.
Mel divided dozens of cookies between 7 classrooms, each
received two dozen. If she had 216 cookies to begin with,
how many dozens did she have left after dividing them up?
Pls help me
Answer:
4 dozen(48)
Step-by-step explanation:
216/dozen(12) =18 dozen(12)
7x2 dozen = 14 dozen
18 dozen - 14 dozen = 4 dozen(48)
Answer:
4
Step-by-step explanation:
Two dozens = 12 × 2 = 24
24 × 7 = 168
216 - 168 = 48
48 ÷ 12 =4
what is the slope and the y intercept?
Need help as soon as possible
Answer:
The answer is C.
Step-by-step explanation:
Given that ∠I and ∠K have the same angles so we can assume that this is an Isoceles Triangle where 2 sides are equal. So we can compare the expressions of JI and JK to get the value of x :
[tex]JI = 5x + 4[/tex]
[tex]JK = 2x + 7[/tex]
[tex]JI = JK[/tex]
[tex]5x + 4 = 2x + 7[/tex]
[tex]5x - 2x = 7 - 4[/tex]
[tex]3x = 3[/tex]
[tex]x = 1[/tex]
Next, we have to substitute the x value into the expression of JK :
[tex]JK = 2(1) + 7[/tex]
[tex]JK = 2 + 7[/tex]
[tex]JK = 9[/tex]
(Correct me if I am wrong)
Consider these numbers, ordered from least to greatest. Negative 1.8, negative 1 and one-fourth, negative 0.2, blank, one-half, 90 percent A number line going from negative 2 to positive 1. Which values could correctly fill in the blank? Select all that apply. 10% 1 -0.1 -1 One-fourth
Answer: Consider these numbers, ordered from least to greatest.
Negative 1.8, negative 1 and one-fourth, negative 0.2, blank, one-half, 90 percent
A number line going from negative 2 to positive 1.
Which values could correctly fill in the blank?
Select all that apply.
Step-by-step explanation:
The values that will correctly fill the blank when ordered from least to greatest on a number line are: 10%, -0.1, and ¼.
The number line given showing different positions of the numbers is shown in the image attached below.
The blank space that was left can only be filled with numbers that are above -0.2 and below 0.5.
From the options given:
10% = 0.1 - this is within -0.2 and 0.5. It will fill the blank.-0.1 and ¼ are also within -0.2 and 0.5. They will also fill the blank.1 and -1 do not fall within -0.2 and 0.5.Therefore the values that will correctly fill the blank when ordered from least to greatest on a number line are: 10%, -0.1, and ¼.
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Which are vertical angles? Check all that apply.
LEAB and BAC
LEAB and CAD
CAD and FAE
_CAB and 2DAE
E
DAC and 2DAE
The answer is b and d
Answer:
Step-by-step explanation:
what are we supposed to check.......and by the way you have written the answer at below too
A map is created on the coordinate plan, lori's house is located at ( -3, 7) and Andreas house is located at (-3,-4). Each unit on the map represents 0.2 mile.
Answer: 2.2 miles.
Step-by-step explanation:
I guess that we want to find the distance between Lori's and Andrea's houses.
First, we have the locations:
L = (-3, 7)
A = (-3. -4)
To find the distance (in units) between two coordinate points (a1, a2) and (b1 b2) we can use the formula:
Distance = I (a1, a2) - (b1, b2)I = √( (a1 - b1)^2 + (a2 - b2)^2)
Then in this case we have that:
Distance = √( ( -3 -(-3))^2 + (7 - (-4))^2) = √( 0 + 11^2) = 11
The distance between their houses is 11 units.
And we know that each unit represents 0.2 miles, then 11 units represent 11 times that amount, the distance in miles will be:
D = 11*0.2 miles = 2.2 miles.
PLEASE HELP ME !!
Instructions: Using the image, find the midpoint of the line segment. Reduce all fractions and enter using a forward slash (i.e. "/").
Answer:
the mid point is ( 3, -1 )
Step-by-step explanation:
the x axis it's 3 and for the y axis is -1