1/3 * 420 = amount of t-shirts sold in the morning
1/3 * 420 = 420/3 = 140 t-shirts
140 t-shirts were sold, so remaining is 420 - 140
420 - 140 = 280 remaining t-shirts
4/7 * 280 = amount of t-shirts sold in the afternoon
4/7 * 280 = (280/7) * 4 = 40 * 4 = 160 t-shirts
160 t-shirts were sold, so remaining is 280 - 160
the remaining t-shirts = 120 t-shirts
120 t-shirts are left to sell at the end of the day
The area of undeveloped land in a suburban town is decreasing at a rate of 17.3% annually. in 2016, there were 3,400 acres of undeveloped land. if t represents the number of years since 2016, which equation can be used to determine after how many years the town will have 900 acres of undeveloped land remaining?
Based on the rate of decrease and the acres of undeveloped land, the equation to determine the number of years till 900 acres is remaining is B)900 = 3,400(0.827)^t.
Which equation shows the number of years till 900 acres are remaining?As 900 acres is the target number of acres to remain, this will be on the left side of the equation as the y value.
The right side of the equation would be:
= Current number of acres remaining x ( 1 - rate of decrease) ^ number of years
= 3,400 x ( 1 - 17.3%) ^ number of years
Putting them together:
900 = 3,400(0.827)^t.
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Work out
the area of this circle. Take
(Pi) to be
3.142 and give your answer to
2 decimal places.
11.2cm
9. Which function's graph is a translation of the graph of f(x) = x shifted 7 units to the left?
Answer:
b) g(x) = x + 7
it may seem like its x - 7, but it's actually x + 7 since it shifts up the graph 7 units.
How do I draw a 50 degree angle ?
To draw a 50 degree angle with a protactor, proceed as follows :
Draw a straight line (i.e. an arm of the angle).Place a dot at one end of the arm. This dot represents the vertex of the angle.Place the centre of the protractor at the vertex dot and the baseline of the protractor along the arm of the angle.Find 50 degree angle on the scale and then mark a small dot at the edge of the protractor.Join the small dot to the vertex with a ruler to form the second arm of the angle.Label the angle with capital letters.Remember that 50 degree angle cannot be constructed using compass.
△ABC ≅ △DEF.
Find the measures of the given angles or the lengths of the given angles.
1). m∠B=3y, m∠E=6y-12
2). AC=7a+5, DF=5a+9
The measures for the given angles B and E are 12° .
Similarity TriangleTriangles are similar when the correspondent angles and the ratio of correspondent sides are equal. Also, it must present the same shape, but it is not mandatory the same dimension.
Like the triangles are similar, ∠B=∠E. Then,
∠B=∠E
3y=6y-12
3y-6y=-12
-3y=-12
y=4
You can write too:
AC=DF
7a+5=5a+9
7a-5a=9-5
2a=4
a=2
Therefore,
∠B=3y= 3* 4 =12
m∠E=6y-12=6*4-12=21-12=12
AC=7a+5= 7*2+5=14+5=19
DF=5a+9=5*2+9=10+9=19
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Which equation can be used to find A, the area of the parallelogram shown?
Explanation:
The area of a parallelogram is equal to base times height.
The base and height are always perpendicular to one another. Usually the base is horizontal along the ground (if not then you'd need to rotate your paper until it is, but that step is optional).
The base is 6 meters and the height is 7 meters.
Therefore, area = base x height = 6 x 7
The side of 11 meters is not used at all. It's likely put in there as a distraction.
Answer:
A = 6 * 7
Step-by-step explanation:
A parallelogram follows the same rules as a regular quadrilateral, as the only difference is that both its sides have been moved along.
1/4 of the students in guitar class attended class today. Only 3/4 of the students share guitars. What fraction of the class shares guitars?
Answer:
3/16 of the class share guitars today.
Step-by-step explanation:
1/4 x 3/4 = 3/16! :)
Tajiq spent $75 on clothes they bought a shirt and three pants. If the shirt cost $15 how much was each pair of pants if they all were the same price? Show your work
Answer:
each pair of pants was $20 each
Step-by-step explanation:
75-15=60
60/3=20
Which quadratic model best represents the data? f(x) = –16x2 99x 6 f(x) = –36x2 37x 5 f(x) = 36x2 37x 5 f(x) = 16x2 99x 6
The quadratic model that represents the data will be A. -16x² - 99x + 6.
What is a quadratic model?It should be noted that a quadratic model simply means a model that is represented by a quadratic equation in the form of y = ax² + bx + c.
From the complete question, the quadratic model that represents the data will be -16x² - 99x + 6.
In conclusion, the correct option is A.
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Answer:
Step-by-step explanation:
Hoping to increase pizza sales on Tuesdays, a new pizza restaurant prints and disperses the following coupon through email and fliers in a neighborhood marketing magazine
After ten weeks of the coupon offer, the owner of the restaurant needs to decide if the restaurant should continue to run the same special or offer a new one. Use the data collected in the table to determine whether or not the coupon appears to be generating sales for the restaurant.
Week Total
Sales
1 $859
2 $1,176
3 $1,480
4 $1,365
5 $1,576
6 $1,498
7 $1,180
8 $1,964
9 $1,634
10 $1,580
Part A: don’t answer
Part B: Use the total sales for weeks 4 and 9 to write an equation for the line of best fit. In your final answer, include all of your calculations.
Part C: in terms of the slope of the equation for the line of best fit, explain whether or not you think the coupon is responsible for the restaurant's increase or decrease in pizza sales on Tuesdays. Use complete sentences in your answer.
Part D: Assuming that the pizza restaurant wishes to continue the coupon for an additional five weeks, use the equation for the line of best fit to predict the restaurant's sales for the Tuesday of the 15th week.
—
B) y = 53.8x + 1149.8
C) Total Sales increase from one week to the next by $53.8.
Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
D) The restaurant's sales for the Monday of the 15th week is expected to be $1956.8
What is equation of line?The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.
B) As by scatter plot,
The total sales for week 4 is given as 1,365 while that of week 9 is 1,634.
Therefore, we shall determine the equation for the line of best fit using the points;
( 4, 1365) and ( 9, 1634)
The first step would be to determine the slope of this line;
slope = (1634 - 1365)/ (9 - 4)
= 53.8
The equation of the line in slope-intercept form is thus;
Sales = 53.8(Week) + c
We need to determine c, the y-intercept. We can use the point ( 4, 1365);
1365= 53.8(4) + c
c = 1365-215.2
c = 1149.8
The equation of the line of best fit is thus;
y = 53.8x + 1149.8
C) The slope of the equation for the lines of best fit was found to be 53.8.
This value is positive which implies
Total Sales increase from one week to the next by $53.8.
The slope in regression is defined as the change in y for every unit change in x.
Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
D) The equation for the line of best fit was found to be;
y = 53.8x+ 1149.8
where y denotes the total sales and x the corresponding week. We are required to determine y when x is 15;
y = 53.8(15) + 1149.8
y = 1956.8
Therefore, the restaurant's sales for the Monday of the 15th week is expected to be $1956.8.
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The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price is each comb being sold? startlayout enlarged left-brace 1st row y = startfraction x over 2 endfraction 2nd row y = negative 0.03 (x minus 95) squared 550 $0.03 $0.50 $0.95 $2.00
The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The linear equation y = x/2 models the income, in dollars, from selling x plastic combs. Hence:
Price of each comb = (x/2) / x = 0.5
The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2
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Answer: B. $0.50
Step-by-step explanation:
Took the Test/Exam
Help asap.
Given the expression: 5x^10 − 80x^2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B:Factor the entire expression completely. Show the steps of your work. (6 points)
Answer:
5x² ( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )
Step-by-step explanation:
→ Find the highest common factor from 5 and 80
5
→ Find the highest common factor of x¹⁰ and x²
x²
→ Write the partially factored form
5x² ( x⁸ - 16 )
→ Factor down ( x⁸ - 16 )
( x⁴ + 4 ) ( x⁴ - 4 )
→ Factor down ( x⁴ + 4 ) ( x⁴ - 4 )
( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )
Answer:
5x^2(x^8 -16)5x^2(x^2 +2x +2)(x^2 -2x +2)(x^2 +2)(x^2 -2)Step-by-step explanation:
The greatest common factor is that factor that includes every prime factor that is found in both expressions. Once that is removed, the formula for the factorization of the difference of squares is needed.
__
AEach expression factors as ...
5x^10 = 5·x^2·x^8
80x^2 = 5·x^2·16
The common factors in these expressions are 5, x^2, so the expression with the greatest common factor factored out is ...
5x^2(x^8 -16)
__
BThe remaining factor is the difference of squares, which factors as ...
a² -b² = (a -b)(a +b)
Here, we have a=x^4 and b=2^2, so the factors of the difference are ...
x^8 -16 = (x^4 -4)(x^4 +4)
The first of these factors is also recognizable as a difference of squares, so it can be factored further:
x^4 -4 = (x^2 -2)(x^2 +2)
The second factor can also be cast as the difference of squares, allowing it to be factored further:
x^4 +4 = (x^4 +4x^2 +4) -(4x^2) = (x^2 +2)^ -(2x)^2
= (x^2 +2x +2)(x^2 -2x +2)
So, the complete factorization of the original expression is ...
5x^10 -80x^2 = 5x^2(x^2 +2x +2)(x^2 -2x +2)(x^2 +2)(x^2 -2)
_____
Additional comment
We could factor to linear terms if we wanted to use radicals and complex numbers. This is the factorization in integers.
Need help with my Study Island math. Wh I can help?
Step-by-step explanation:
scientific notation is
a.b × 10^c
with a being <> 0.
0.0002 cm = 2.0×10^-4 cm (the "2" moves 4 positions to the right for the actual number).
so, this is between 1.0×10^-4 cm and 1.0×10^-3 cm.
0.02 cm = 2.0×10^-2 cm (the "2" only need to move 2 positions to the right for the actual number).
so, this is between 1.0×10-2 cm and 1.0×10^-1 cm.
200 cm = 2.0×10² cm (now the "2" needs to move 2 positions to the left for the actual number).
so, this is between 1.0×10² cm and 1.0×10³ cm.
20,000 cm = 2.0×10⁴ cm (the "2" has to move 4 positions to the left for the actual number).
so, this is between 1.0×10⁴ cm and 1.0×10⁵ cm.
PLEASE HELP WILL MARK BRAINLIEST
8-10
Answer:
[8] Area is = to 1017.36 Circumference is = to 113.04
[9] Area is = 490.625 Circumference is = 78.5
[10] D = 16 R = 8
Step-by-step explanation:
[8]
Area is = to 1017.36
Circumference is = to 113.04
Formula:
Area = πr²
Circumference = 2πr
Solve:
A = πr²
A = 3.14(18) ²
A = 3.14(324)
A = 1017.36
C= 2πr
C = 2(3.14)(18)
C = 113.04
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Area = 490.625
Circumference is = 78.5
Formula:
Area = πr²
Circumference = 2πr
Solve:
Area = πr²
A = 3.14(12.5)²
A = 3.14(156.25)
A = 490.625
Circumference = 2πr
C = 2(3.14)(12.5)
C = 78.5
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
[10]
Circle area = π * r² = π * 64 [cm²] ≈ 201.06 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 8 [cm] * 2 = 16 [cm]
Hence,
D = 16
R = 8
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Kavinsky
If no digit can be used more than once, find how many numbers that can be formed from the digits 3, 4, 5, 6, 7, 8 are greater than 7000.
Answer:
1 560
Step-by-step explanation:
If no digit (from the digits 3, 4, 5, 6, 7, 8) can be used more than once :
we can form 6P5 = 720 (five-digit numbers) and they are all > 7000
we can form 6P6 = 720 (six-digit numbers) and they are all > 7000
if our number has four digits ,then the digit in the ten-thousands place of it must be 7 or 8 :
In this case :
we can form 5P3=60 number where the digit in the ten-thousands place of it is 7.
and we can form 5P3=60 number where the digit in the ten-thousands place of it is 8.
Final answer :
We can form 720+720+60+60 = 1 560 number greater than 7000
Factor 6x^2+14x.
Please, help
Factor 2x from 6x².
2x (3x)+14x
Factor 2x from 14x.
2x (3x) + 2x (7)
Factor 2x from 2x (3x) + 2x (7).
2x(3x+7) ====> Answers
Answer:
(2x)(3x + 7)
Step-by-step explanation:
Hello!
We can factor this expression by taking out the GCF of both the terms.
The GCF is 2x, because it is the largest factor that is in common between 6x² and 14x
Factor6x² + 14x2x(3x) + 2x(7)(2x)(3x + 7)The factored expression is (2x)(3x + 7)
please help me outttt
Answer:
(-1, 4) and (2, 7)
Step-by-step explanation:
Graphs f(x) & g (x) are intersecting each other.-> f(x) = g(x)[tex]\implies x^2+3 =x + 5[/tex][tex]\implies x^2+3 -x -5=0[/tex][tex]\implies x^2 -x -2=0[/tex][tex]\implies x^2 -2x +x-2=0[/tex][tex]\implies x(x -2) +1(x-2)=0[/tex][tex]\implies (x -2)(x+1)=0[/tex][tex]\implies (x -2)=0,\:\: (x+1)=0[/tex][tex]\implies x=2\:\: x=-1[/tex][tex]\implies x=-1,\:\:2[/tex]When x = -1[tex]f(x) = (-1)^2+3 = 1 +3 = 4 [/tex]-> (x, f(x)) = (-1, 4) & When x = 2[tex]f(x) = (2)^2+3 = 4 +3 = 7 [/tex]-> (x, f(x)) = (2, 7) Thus, the points of intersection of the functions f(x) and g(x) are (-1, 4) and (2, 7)Find (a) arc length and (b) Area of a sector.
Answer:
a) 19.63 mm (2 dp)
b) 245.44 mm² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]
[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]
Calculation
Given:
[tex]\theta[/tex] = 45°r = 25 mm[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (25)\left(\dfrac{45^{\circ}}{360^{\circ}}\right)\\ & = 50 \pi \left(\dfrac{1}{8}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf mm \:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{45^{\circ}}{360^{\circ}}\right) \pi (25)^2\\& = \left(\dfrac{1}{8}\right)\pi \cdot 625\\& = \dfrac{625}{8} \pi\\& = 245.44\: \sf mm^2 \:(2\:dp)\end{aligned}[/tex]
Please note: As you have not specified if π should be approximated, I have not used an approximation for π.
You invest $2000 compounded monthly at 9%, how much money do you have in 10 years?
Answer: The final balance is $4,734.73
Greenwood Middle School is having a math competition. Four students are called to the stand to answer a question. The question is:
51.32 – 11.98
Answer: 39.34
Step-by-step explanation:
Select the correct answer from each drop-down menu. a container holds 50 electronic components, of which 10 are defective. if 6 components are drawn at random from the container, the probability that at least 4 are not defective is . if 8 components are drawn at random from the container, the probability that exactly 3 of them are defective is .
The probability of exactly 3 of the containers being defective is given as 0.1468
How to solve for the probabilityWe have to set p as the probability of container being non- defective
We have p as the probability of container being defective 50 - 10 = 40
p = 40/50
= 0.8
q = 10/50
= 0.2
P(3) = 8c3 * 0.2² * 0.8⁵
= 0.1468
Hence the probability that the container has exactly 3 defective containers is 0.1468
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Alexa danced for 3 2/4 hours on Saturday. Sherlyn swam 1/5 of that time. How many
hours did Sherlyn swim on Saturday?
Answer:
Sherlyn swam 42 minutes on Saturday
Step-by-step explanation:
danced for 3 2/4 hours on Saturday
3 2/4 hours is equivalent to 3.5 hours
1 / 5 of (that time) 3.5 hours is (1 / 5) * 3.5 = 0.7 hours
Because one hour is equal to sixty minutes, in order to change the units you have to multiply the number of hours, 0.7, by 60.
0.7 x 60 = 42 minutes
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Cube: Find the surface area of a cube with side 5 inches.
Answer:
We are given the dimension of the side being 5 inches and it states that we need to determine the surface area. The first step that we must do is find the area of one side and then we multiply it by 6 because we have 6 same sides.
[tex]A = s^2[/tex]
[tex]A = (5\ in)^2[/tex]
[tex]A = 25\ in^2[/tex]
Now that we have the area of one side we can multiply it by 6 to get the total surface area.
[tex]A = 25\ in^2 * 6[/tex]
[tex]A = 150\ in^2[/tex]
Therefore, our final answer is that the surface area is 150 inches squared
Hope this helps!
Answer:
150 square inches
Step-by-step explanation:
find the area of 1 square face
5*5=25
multiply by 6 faces
25*6=150
30 points!! What is the equation of this line?
Answer:
y = - 2x
Step-by-step explanation:
the equation of a line passing through the origin is
y = mx ( m is the slope )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 1, 2) ← 2 points on the line
m = [tex]\frac{2-0}{-1-0}[/tex] = [tex]\frac{2}{-1}[/tex] = - 2 , then
y = - 2x ← equation of line
In ΔABC, m∠B = 90°, cos(C) = , and AB = 16 units.
Based on this information, m∠A =
°, m∠C =
°, and AC =
units.
Note that the angle measures are rounded to the nearest degree.
The sides and angles of the right triangle area as follows:
m∠C = 28°
m∠A = 62°
AC = 17 units
How to find the sides and angles of a right angle triangle?Using trigonometric ratios,
cos C = 15 / 17
m∠C = cos⁻¹ 0.88235294117
m∠C = 28.0726015272
m∠C = 28°
m∠A = 180 - 28 - 90 = 62°
AC = 17 units
AC is the hypotenuse of the right angle triangle.
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In a board game, there is a 29 chance of drawing a card that gives a player a double turn. The remaining cards are single-turn cards. A player wants to run a simulation to estimate the probability of drawing two double-turn cards in a row, assuming the first card is replaced, and the deck is shuffled afterward.
Probability helps us to know the chances of an event occurring. The probability of getting a double card in a row is 0.311.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of drawing a single double turn card for the first time, therefore,
Probability = 29/52
Further, given the card is replaced and reshuffled, therefore, the probability of getting a double card again will be,
Probability = 29/52
Thus, the probability of getting a double card in a row can be written as,
Probability = (29/52)×(29/52) = 0.311
Hence, the probability of getting a double card in a row is 0.311.
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Evaluate the following expression. 7^0=?
Answer:
1
Step-by-step explanation:
7^0 = 1
Note : -
( Any number )^0 = 1
Which shapes contain at least one right angle?
Select each correct answer.
Answer:
in the picture
Step-by-step explanation:
the sign you see at the corners with arrows (see drawing) indicate a right angle
Consider the following function f(x) = x² + 5.
Part A: Write a function, in vertex form, that shifts f(x) right 3 units.
Part B: Write a function, in vertex form, that shifts f(x) left 10 units.
Part A
To shift the curve 3 units to the right, we'll replace x with x-3. What this does is move the xy axis 3 units to the left. If we held the curve in place as the axis moves, then it gives the illusion the curve is moving 3 units to the right.
[tex]f(x) = x^2 + 5\\\\f(x-3) = (x-3)^2 + 5\\\\g(x) = (x-3)^2 + 5\\\\[/tex]
Do not expand out the (x-3)^2 term, because you want to keep the function in vertex form. The old vertex of (0,5) moves three units to the right to arrive at (3,5)
Answer: [tex]g(x) = (x-3)^2 + 5[/tex]==============================================================
Part B
We use the same idea as before. This time we're moving the curve 10 units to the left, so we'll replace x with x+10
[tex]f(x) = x^2 + 5\\\\f(x+10) = (x+10)^2 + 5\\\\g(x) = (x+10)^2 + 5\\\\[/tex]
Look at the image!
iready
a =80 vertically oposite angle
a+b=180 angle of the same side of transversal are 180 degree
so b=180-80
=100
c=b vertically oposite angle
b=100=c
c= 100
I hope it's helpful for you
Answer:
a=80, b=100, c=100
Step-by-step explanation:
Because A is directly across from 80 degrees, A is also 80 degrees. They are alternate angles, and so they equal the same thing. B is 100, because it is on the same line as 80, and a line equals 180 degrees. C is also 100 degrees, because it is across from B and on the same line as A, which is 80 degrees.
Hope this helps!