At the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 cheeses
Answer:
Diego can choose the 15 items in 128 different ways.
Step-by-step explanation:
Since at the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads, and he wants to use the Express Lane, so he can only buy 15 items, to determine how many ways can he choose which 15 items to buy if he wants all 6 cheeses the following calculation must be performed:
4 x 4 x 8 = X
16 x 8 = X
128 = X
Therefore, Diego can choose the 15 items in 128 different ways.
Please help I will give you Brainlyest
Answer:
below
Step-by-step explanation:
Clare's mistake was the writing of 4000 in standard form
he wrote 4 ×10²
instead of 4 ×10³
Answer:
Step 1
Step-by-step explanation:
I believe Claire's mistake is when she tries to simplify 4000
She says that 4000 = 4 × 10²
4000 is actually equal to 4 ×10³
Write the word sentence as an inequality.
3.2 less than a number t is at most 7.5
t-3.2 ≤ 7.5
"at most" means less than or equal to
A farmer finds that if she plants 55 trees per acre, each tree will yield 25 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. How many trees should she plant per acre to maximize her harvest
Answer:
31 trees per acre will maximize the harvest
Step-by-step explanation:
Given
[tex]Plant \to 55[/tex] trees/acre
[tex]Yield \to 25[/tex] bushels
[tex]x \to trees[/tex]
Required
Number of trees to maximize harvest
From the question, we understand that:
Yield will decrease by 4 i.e. 25 - 4x
For every additional tree planted, i.e. 55 + x
So, the function is:
[tex]F(x) = (25- 4x)*(55+x)[/tex]
Open bracket
[tex]F(x) = 25 * 55 -4x * 55 + 25 * x -4x*x[/tex]
[tex]F(x) = 1375 - 220x + 25x -4x^2[/tex]
[tex]F(x) = 1375 -195x -4x^2[/tex]
Rewrite as:
[tex]F(x) = -4x^2 -195x +1375[/tex]
The maximum of a quadratic function is calculated as:
[tex]Max = -\frac{b}{2a}[/tex]
In the above equation:
[tex]a = -4; b =-195; c = 1375[/tex]
So:
[tex]x = -\frac{-195}{2 * -4}[/tex]
[tex]x = -\frac{195}{8}[/tex]
[tex]x = -24.375[/tex]
Recall that the number of trees to be planted is: 55 + x
So, we have:
[tex]Trees = 55+x[/tex]
[tex]Trees = 55-24.375[/tex]
[tex]Trees = 30.625[/tex]
Approximate
[tex]Trees = 31[/tex]
Hello please help me solve this inequality shown in the graph, thank you so much!
Olivia randomly samples 50 students attending a basketball game and asks what grade they are in. Of the studets surveyed, 19 were in the seventh grade. I
there are 200 students attending the basketball game, based on the sample, how many of them are in seventh grade?
Answer:
76
Step-by-step explanation:
19 out of 50 are in 7th grade.
200/50 = 4
Multiply both numbers in the ratio by 4.
19 out of 50 = 76 out of 200
Answer: 76
For numbers 6-10, how long does it take to travel:
11. A car travels 200 kilometers in 8 hours. Calculate the average speed of the car in:
a. Kilometer per hour
b. Kilometers per minute
This question have no choices specify your answers only
Answer:
A
Step-by-step explanation:
You divide distance over time so 200 divided by 8.
What is the slope formula?
Answer:
(y2-y1)/(x2-x1)
Step-by-step explanation:
The slope is the change in y over the change in x
(y2-y1)/(x2-x1)
where ( x1,y1) and (x2,y2) are two points on the line
Answer:
O A. [tex]\frac{y2-y1}{x2-x1}[/tex]
Step-by-step explanation:
This is just about how the Slope-Formula works
ok so you get two points off a graph then you use it to plot it in the Slope-Formula like this
for example imma go with (-2, 5) and (3, 7)
I need to subtract 7 - 5 / 3 - -2. so...
m = slope
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{7-5}{3--2}[/tex] Only add the denominators when there's 2 - signs together
m = [tex]\frac{2}{5}[/tex]
A jogger travelled 52km in 4 days.what is the rate he travelled per day?
52km multiply by 4(days)=208
convert 6 miles to meters
Answer:
9656.06 meters
Step-by-step explanation:
Anna invested 2,500 at an annual rate 5%. How long will it take until anna earns 1,125 in interest
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Answer:
9 years
Step-by-step explanation:
The simple interest formula is ...
I = Prt
where I is the interest earned on principal P invested at annual rate r for t years. Solving for t, we have ...
t = I/(Pr) = 1125/(2500×.05) = 1125/125
t = 9 . . . . years
It will take 9 years for Anna to earn 1125 in interest.
Which values for A and B will create many solutions for this system of equations? 4x-Ay=15 -4x+6y=B
Answer:
A = 6; B = -15
Step-by-step explanation:
To have an infinite number of solutions, both equations must be the same.
4x - Ay = 15
-4x + 6y = B
The only coefficient we see in both equations is the coefficient of the x term. We have -4x and 4x. Multiply both sides of the second equation by -1.
4x - Ay = 15
4x - 6y = -B
For the equation to be equal, we need each term of one equation to be equal to the corresponding term of the other equation.
4x and 4x are equal.
-Ay must equal -6y
-Ay = -6y
-A = -6
A = 6
15 must equal -B
-B = 15
B = -15
Answer: A = 6; B = -15
How can I describe an angle's measure?
The in center is the center of the circle of a triangle
1) circumscribed
2) centralized
3) cocentric
4) inscribed
Answer:
inscribed
Step-by-step explanation:
For any given triangle, the circle inside of it is called the Inscribed circle
Solve the inequality 5u≤8u−21 and write the solution in interval notation
Answer:
Step-by-step explanation:
[tex]5u\leq 8u-21[/tex]
Subtract 8u from both sides
[tex]-3u\leq -21[/tex]
Divide by -3 on both sides
[tex]u\geq 7[/tex]
Interval notation: [greater/less than or equal to], (greater or equal to)
[7,∞)
The solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).
What is inequality?In mathematics, an inequality is a remark that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
Here,
To solve the inequality 5u ≤ 8u - 21, we can start by isolating u on one side of the inequality. We can do this by subtracting 5u from both sides:
5u ≤ 8u - 21
-3u ≤ -21
Divide both sides by -3. Note that dividing by a negative number will reverse the direction of the inequality:
u ≥ 7
Therefore, the solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).
Learn more about inequality here:
brainly.com/question/14098842
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HELP I will give brainliest I am begging you only a few questions
Answer:
Graph A: (0,10) Graph B: (0,20)
Graph A: Height (feet) Graph B: Hight (feet)
Graph A: 138 Graph B: 120
Graph A: 32.6 Graph B: 43
Step-by-step explanation:
The smaller text was really blurry but I tried my best. Hope this helps!
Answer:
Step-by-step explanation:
I just pointed the answers, but quality of picture is poor: it's impossible to indicate the numbers on y-axis, and tell exact number on x-axis.
Find the surface area of the regular pyramid.
Answer:
B
Step-by-step explanation:
Base area = side^2 = 3^2 = 9 m^2
Base perimeter = side x 4 = 3 x 4 = 12 m
LA = (base perimeter x slant height)/2 = (12 x 5)/2 = 30 m
SA = base area + LA = 9 + 30 = 39 m^2
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes with the results shown in the table below.
Complete parts (a) and (b)
Arrivals Frequency
0 21
1 46
2 40
3 36
4 25
5 20
6 8
7 3
8 1
a. Compute the expected number of arrivals per minute.
μ=___( please type as an integer or a decimal)
b. Compute the standard deviation
σ=___(please round to three decimal places as needed)
Answer:
a. μ = 25
b. σ = 16.496
Step-by-step explanation:
Note: See the attached excel for the calculation of Mean and Deviation from Mean.
Let: N = Number of observation = 9
F = Frequency
Therefore, we have:
a. Compute the expected number of arrivals per minute. μ=___( please type as an integer or a decimal)
From the attached excel file, we have:
Total F = 200
Therefore, we have:
μ = Mean = Total of F / (N - 1) = 200 / (9 - 1) = 25
b. Compute the standard deviation σ=___(please round to three decimal places as needed)
From the attached excel file, we have:
Total (F - μ)^2 = 2,177
σ = Standard deviation = (Total of (F - μ)^2 / (N - 1))^0.5 = (2,177 / (9 - 1))^0.5 = 16.496
evaluate the expression when f=6 12f+3
Answer:
75
Step-by-step explanation:
Substitute 6 for f
12f+3=
12*6+3=
72 + 3 = 75
Answer:
12f+3 = 75 when f = 6
Step-by-step explanation:
12f+3
Let f = 6
12*6+3
Multiply
72 +3
Add
75
(0.020(5/4) + 3 ((1/5) – (1/4)))
Answer:
- 0.125
Step-by-step explanation:
Given the equation :
(0.020(5/4) + 3 ((1/5) – (1/4)))
0.020(5/4) = 0.025
3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15
0.025 + - 0.15 = 0.025 - 0.15 = - 0.125
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s. At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
Answer:
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Step-by-step explanation:
Volume of a right circular cone:
The volume of a right circular cone, with radius r and height h, is given by the following formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Implicit derivation:
To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
Radius is 107 in. and the height is 151 in.
This means that [tex]r = 107, h = 151[/tex]
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.
This means that [tex]\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6[/tex]
At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
This is [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))[/tex]
[tex]\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}[/tex]
[tex]\frac{dV}{dt} = 1926[/tex]
Positive, so increasing.
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
What is the length of u and v in this 30-60-90 triangle
Answer:
option 2
Step-by-step explanation:
Using trigonometric ratio:
[tex]Cos \ 60 = \frac{adjacent } {hypotenuse} \\\\\frac{1}{2} = \frac{4}{u}\\\\1 \times u = 2 \times 4 \\\\u = 8[/tex]
Now using Pythagoras theorem we will find v
[tex]8^2 = 4^2 + v^2\\\\64 = 16 + v^2\\\\v^2 = 64 - 16 \\\\v = \sqrt{48} = \sqrt{16 \times 3} = \sqrt{4^2 \times 3 } = 4\sqrt{3}[/tex]
By using trigonometric relations, we will see that v = 4*√3 and u = 8
How to get the missing lengths?
Here we have a right triangle, we can use trigonometric relations to find the missing sides.
We can see that v is the opposite cathetus of the 60° angle, then we can use the relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing what we know, we get:
tan(60°) = v/4
4*tan(60°) = v = 4*√3
To get the value of u, we use:
cos(a) = (adjacent cathetus)/(hypotenuse).
cos(60°) = 4/u
u = 4/cos(60°) = 2*4 = 8
Then we have:
v = 4*√3
u = 8
If you want to learn more about triangles, you can read:
https://brainly.com/question/17972372
Alexander is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.
Over one month, he collected 1297 cans.
What is the mass, in kilograms, of these cans?
Answer:
22 kg
Step-by-step explanation:
1297 cans * (17 grams)/(1 can) * (1 kg)/(1000 g) = 22.049 kg
Answer: 22 kg
What is the slope and y-intercept of 6x-5y=13
Answer:
The slope is 6/5 and the y intercept is -13/5
Step-by-step explanation:
6x-5y=13
Solve for y
Subtract 6x from each side
6x-6x-5y=-6x+13
-5y = -6x+13
Divide by -5
-5y/-5 = -6x/-5 +13/-5
y = +6/5x -13/5
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is 6/5 and the y intercept is -13/5
Which inequality is true?
А. Зп > 9
B. 7 + 8< 11
C. 27 -1 < 5
D. 2 > 2
SUBMIT
< PREVIOUS
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Answer:
А. Зп > 9
Step-by-step explanation:
The inequality of A may or may not be true. (It is true only if n > 3.) All of the others are definitely false.
Find the surface area of a square pyramid with side length 4 yd and slant height 6 yd.
Answer:
112 yd²
Step-by-step explanation:
Surface area of the square pyramid = area of base + perimeter of base × slant height
Area of base = s²
s = 4 yd
Area = 4² = 16 yd²
Perimeter = 4(s)
Perimeter = 4(4) = 16 yd
Slant height = 6 yd
Surface area of the square pyramid = 16 + 16 × 6
= 16 + 96
= 112 yd²
ASAP! see the picture please!!
Answer:
the second one
function A has a slope of 3
function B has a slope of 5
Recounting Rectangles
How many rectangles are
there in the figure below?
Answer:
gimme a second, I'll comment
Find the midpoint of the equation y = 4x - 6 between the x-intercepts and the y-intercepts.
Step-by-step explanation:
y int
x=0
y=4(0)-6
y=-6
0;-6
x int
y=0
0=4x-6
6=4x
6/4=x
3/2=x
3/2;0
Answer:
Below in bold.
Step-by-step explanation:
y = 4x - 6
Find y-intercept:
y = 4(0) - 6 = -6
Y intercept is at (0, -6)
x-intercept:
4x - 6 = 0
4x = 6
x = 6/4 =1.5.
x intercept is at (1.5, 0)
Midpoint is at ((0+1.5)/2, (-6 + 0)/2)
= (0.75, -3)
Zeus Computer Chips, Inc., used to have major contracts to produce the Centrino-type chips. The market has been declining during the past three years because of the quad-core chips, which it cannot produce, so Zeus has the unpleasant task of forecasting next year. The task is unpleasant because the firm has not been able to find replacement chips for its product lines. Here is demand over the past 12 quarters:
Two Years
Ago Last Year This Year
I 4800 I 3500 I 3,200
II 3500 II 2700 II 2100
III 4300 III 3500 III 2700
IV 3,000 IV 2,400 IV 1700
Use the decomposition technique to forecast demand for the next four quarters.
Answer:
1st quarter := 2488.23
2nd quarter = 1646.50
3rd quarter = 1893.98
4th quarter = 1152.93
Step-by-step explanation:
Forecast demand in the next four quarters
intercept ( a ) = 3116.67 - (- 168.25 * 6.5 ) = 4210.29
Slope ( b ) = ( 219041.15 ) - ( 12 * 6.5 * 3,116.67 ) / 650 - ( 12 * ( 6.5)^2 )
= -24059.11 / 143 = -168.25
Forecast demand = a + bt = 4210.29 + 168.25t
1st quarter := 2488.23
2nd quarter = 1646.50
3rd quarter = 1893.98
4th quarter = 1152.93
Values calculated using data from table attached below ( table 2 )