Explanation:
We can do cross multiplying through ratios:
310 feet / 10 secs = x feet / 12 secs
10x = 310 * 12
10x = 3720
x = 372 feet
OR
Divide 310 feet and 10 secs to get 31 feet in 1 sec
Multiply 31 ft and 1 sec to get 372 ft in 12 secs
Solve for x
-2x+6y=13
A Jewelry company makes and sells necklaces. For one type of necklace, the company uses clay beads and glass beads. Each necklace has no more than 10 clay beads and at least 4 glass beads. For every necklace, four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads. Each clay bead costs $0.20 and each glass bead costs $0.40. The company wants to find the minimum cost to make a necklace with clay and glass beads and find the combination of clay and glass beads in a necklace that costs the least to make. a. Define the variables and write a system of inequalities. Then write an equation for the cost C. b. Graph the system of inequalities and find the coordinates of the vertices of the feasible region. c. Find the number of clay beads and glass beads in a necklace that costs the least to make.
a. The system of inequalities that models the situation is:
0 ≤ x ≤ 10.y ≥ 4.4y ≤ 8 + 2x.The equation for the cost is: C(x,y) = 0.2x + 0.4y.
b. The graph is given by the image at the end of the answer, and the vertices are (4,4), (10,4) and (10,7).
c. The number of clay beads and glass beads in a necklace that costs the least to make is: 4 clay beads and 4 glass beads.
What is the system of inequalities?The variables for the system are presented as follows:
Variable x: number of clay beads used.Variable y: number of glass beads used.Each necklace has no more than 10 clay beads and at least 4 glass beads, hence the constraints are listed as follows:
0 ≤ x ≤ 10.y ≥ 4.The numbers of each beads are countable amounts, meaning that they cannot assume negative values.
Four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads, hence the final constraint is of:
4y ≤ 8 + 2x.
Each clay bead costs $0.20 and each glass bead costs $0.40, hence the cost function is given as follows:
C(x,y) = 0.2x + 0.4y.
Using the three constraints, the graph is given by the image at the end of the answer, and the vertices are as follows:
(4,4).(10,4).(10,7).The minimum cost is at the vertex with the smallest numeric value of the cost function, hence the numeric values are listed as follows:
C(4,4) = 0.2(4) + 0.4(4) = 2.4. -> minimum cost.C(10,4) = 0.2(10) + 0.4(4) = 3.6.C(10,7) = 0.2(10) + 0.4(7) = 4.8.More can be learned about a system of inequalities at https://brainly.com/question/9195260
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1) A sales representative earns a 2.5% commission on sales. Find the commission earned when the total sales are $80,500.
The last time that Dr. Mason, a farm veterinarian, checked, a particular pig weighed 59.8 kilograms. Dr. Mason just weighed the pig again and found out that it weighs 8.1% less now. How much does the pig weigh now
The weight of the pig now is 54.9562 kg.
How to calculate the weight?Given that the farm veterinarian, checked, a particular pig weighed 59.8 kilograms. Dr. Mason just weighed the pig again and found out that it weighs 8.1% less now.
The reduction will be:
= Percentage × Original weight
= 8.1% × 59.8
= 4.8438 kg
Therefore the weight of the pig will be:
= Original weight - Reduction
= 59.8 - 4.8438
= 54.9562 kg
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Find the equation of a line parallel to 2x + 2y = -12 that passes through the
point (2, -7).
y+7=x-2
y+7=(x - 2)
y-7=x+2
y - 7 = -(x + 2)
The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2) , the correct option is (b) .
In the question ,
it is given that ,
the equation of the line is parallel to 2x + 2y = -12 ,
2x + 2y = 12
2y = -2x + 12
Dividing both sides by 2 , we get
y = -x + 6
So , the slope of the line is -1 ,
since the required line is parallel , so the slope of the required line is -1 .
So , the equation of the line passing through the points (2,-7) with slope -1 is
(y - y₁) = m(x - x₁)
(y -(-7)) = -1(x - 2)
y + 7 = -1(x - 2)
y + 7 = -(x - 2)
Therefore , The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2) .
The given question is incomplete , the complete question is
Find the equation of a line parallel to 2x + 2y = -12 that passes through the point (2, -7) ?
(a) y+7=x-2
(b) y+7= -(x - 2)
(c) y-7=x+2
(d) y-7= -(x + 2)
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Simplify
a9/a5
a^4
1/a^4
4
a^14
Answer:
36a^10
Step-by-step explanation:
HELP ME PLSS THIS IS DUE NOW
The sum of three times a number and 2 less than 4 times that same number is 15. Which of the followin
equations could be used to find the value of the number, n? Explain how you arrived at your choice.
Answer:
11
Step-by-step explanation:
Three times an unknown number
= 3(n)
Added to
Two less than four times the same unknown number
= 4 - 2(n)
Total
= 3(n) + 4 - 2(n) = 15
= 3n + 4 - 2n = 15
Collect like terms
= 3n - 2n = 15 - 4
n = 11
2 p varies directly as q and the square of r and inversely as s.
a. Write the equation of the relation.
b. Find kif p = 40 when q = 5, r = 4 and s = 6.
c. Find p when q = 8, r= 6 and s= 9.
d. Finds when p= 10, q=5 and r = 2.
The equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex].
The value of k when q = 5, r = 4 and s = 6 is 3.
The value of p when q = 8, r= 6 and s= 9 is 96.
The value of s when p= 10, q=5 and r = 2 is 6.
A connection between two different items is called variation. There are two categories of difference. Direct Variation is the name of the first one. When two variables move in the same direction, direct variation occurs. Additionally, as one variable rises, the other variable rises as well. Inverse Variation is the second kind. When the two variables move in the opposite direction, inverse variation occurs. Additionally, this occurs when one variable rises while the other falls.
Since p varies directly as q and the square of r and inversely as s. So the equation will be [tex]p=k \frac{qr^2}{s}[/tex].
Now, finding the value of k, for p = 40 when q = 5, r = 4 and s = 6,
[tex]p=k \frac{qr^2}{s}\\40=k \frac{5\times4^2}{6}\\k = 3[/tex]
Now, finding the value of p when q = 8, r= 6 and s= 9,
[tex]p=3 \frac{8\times 6^2}{9}\\=96[/tex]
Now, finding the value of s when p= 10, q=5 and r = 2,
[tex]10=3 \frac{5\times 2^2}{s}\\\\10=3\times \frac{20}{s}\\s=6[/tex]
Therefore, the equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex] , the value of k when p = 40 when q = 5, r = 4 and s = 6 is 3, the value of p when q = 8, r= 6 and s= 9 is 96 and the value of s when p= 10, q=5 and r = 2 is 6.
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The tree diagram represents an
experiment consisting of two trials.
P(D) =[?]
Answer:
P(D) = 0.7
Step-by-step explanation:
There are two routes to D:
AD, which is 0.5*0.6BD, which is 0.5*0.7We then add these two probabilities:
AD + BD = (0.5*0.6) + (0.5*0.7) = 0.3 + 0.35 = 0.7
Therefore, P(D) should be 0.7, or 70%
Franchising is a popular way to grow. Subway has about 42,000 franchisees that pay 12. 5% of their annual store revenue ($417,000 average) to subway. About how much does subway collect in franchise fees?.
Total amount that Subway collect in franchise fees = $2,189,250,000
Total number of subway franchisees = 42,000
Average annual store revenue = $417,000
Total paying percentage of franchisees = 12.5%
12.5% of average revenue = (417000×12.5)÷100
= $52,125
Total subway collection in franchise fee= total number of franchisees×amount of fees per franchisees
= 42,000×52,125
= $2,189,250,000
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Since subways has about 42000 franchisees and about $417000 average revenue is earned. Therefore, the total amount that Subway collect in franchise fees is $2,189,250,000.
Subways Franchise operate 16 submarine sandwich shop and they expanded quickly with its long time slogan "East Fresh".
Franchisor gives a franchisee the authority to do business in the franchisor's trade name using its business system it is called franchising.
Subways franchises pay 12.5% every week (gross sales minus the sales tax), 8% goes toward the franchise royalties and 45% gores towards advertising.
The company has the lowest start-up costs compared to many other fast food franchises but does take more royalty and advertising money.
The franchise fee:
A franchise owner pay 12.5% of gross sales minus tax every week. They must pay even if they are losing money.8% of that 12.5% goes toward the franchise royalties and 4.5% is for advertising.Now, according to the question:
Total number of subway franchisees = 42,000
Average annual store revenue = $417,000
Total paying percentage of franchisees = 12.5%
∴ At 12.5% of average revenue = (417000 × 12.5) ÷ 100
= $52,125
Total subway collection in franchise fee
= total number of franchisees × amount of fees per franchises
= 42,000×52,125
= $2,189,250,000
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Solve the equation by factoring.
(x+2)(x + 7) = 0
A) (-2,-7)
C) (5,-8)
B) -5,5)
D) (6, 3)
Step-by-step explanation:
(x+2)(x+7) = 0
It is already factorised.
So, x = (-2,-7)
So, option A is correct
If you are given the two sides that are not the hypotenuse, which trig function should you use?.
The trigonometric function that can be used when given 2 sides that are not the hypotenuse is tangent.
When two sides are given that is not the hypotenuse, the trigonometric function that can be employed is the tangent.
A right-angle triangle has the following sides:
Hypotenuse
Adjacent side
the opposite side
The following trigonometric ratios can be used to determine the angles in a right-angle triangle:
sin = opposite/hypotenuse
cos = neighboring / hypotenuse
tan = opposite /adjacent
Tangent is the trigonometric function that can be used to determine the angle of a right-angle triangle given two sides other than the hypotenuse.
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HELP HELP HELP
(2^4x+4) / (2^x+1)
Answer:
[tex]2^{3x+3}[/tex]
Step-by-step explanation:
to divide exponents with the same base you just subtract them
(4x+4)-(X+1)
4x+4-x-1
3x+3
Hopes this helps please mark brainliest
Answer:
frac{16x+4}{2^{x}+1 =
Step-by-step explanation:
Evaluate the exponent! hope this helped
Please someone help me I need help with this
From the given graph we get, the coordinates of original P are (-6,-6).
So initial x=-6 and y=-6
Also from the graph we can see that the coordinates of transformed point P' are (-1,3)
So now, (-1,3) = (-6+5,-6+9) = (x+5,y+9)
Hence the first and second box are 5 and 9 respectively.
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Find the area of the chape giving… pls help me
Answer:
Area = 8 sq cm
Step-by-step explanation:
This shape is a parallelogram. Its like a rectangle that got tipped over. Area is:
base × height.
We don't know the base that is on the bottom of the image as it is shown. But if you turn it sideways, the 4 can be the base and the 2 is the height.
Area = b × h
= 4 × 2
= 8
The area is 8 sq cm.
Write the following decimal in standard form:
twelve and eighty-four hundredths
i really need this asap
Answer:
below
Step-by-step explanation:
12 + 84/100 = 12.84
a survey carried out recently to find the number of applicants that apply for jobs in three newspaper establishment revealed i-70 applied to the Daily Times 65 applied to the daily graphic and 85 apply to the Punch. 40 applied to the daily times only, 20 applied to the daily graphic only while 45 applied to the punch only. if 15 applied to all the three newspaper establishment, find: I. the number that applied to both the daily times and daily graphic. Ii.the number that applied to the daily times and the punch. III. the number that applied to both the daily graphic and the punch. iv. the number that applied to at least one newspaper establishment.
The values of x= 10; y= 5; z= 20.
Given that
40 applied to the daily times only,
20 applied to the daily graphic only while
45 applied to the punch only.
To find out, if 15 applied to all the three newspaper establishment
I. the number that applied to both the daily times and daily graphic
II. the number that applied to the daily times and the punch.
III. the number that applied to both the daily graphic and the punch.
iv. the number that applied to at least one newspaper establishment.
Given that: DT (marked "T"), 70 & 40 (red circle).
DG (marked "G"), 65 & 20 (green circle).
P, 85 & 45 (blue circle).
x + y + 15 + 40 = 70
y + z + 15 + 45 = 85
x + z + 15 + 20 = 65
==========>
x + y = 15, (1)
y + z = 25, (2)
x + z = 30. (3)
------------------------Add 3 equations ====>
2x + 2y + 2z = 15 + 25 + 30 = 70 ====>
x + y + z = 35. (4)
Subtract (1) from (4): z= 20;
Subtract (2) from (4): x= 10;
Subtract (3) from (4): y= 5.
Hence the answer is the values of x= 10; y= 5; z= 20.
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Please, i need help . .
Step-by-step explanation:
b^3 x b^8 / b^5
b^11/b^5
b^(11-5)
b^6
Please I need help please
The measure of missing angles in the diagram is angle 1 = 88°, angle 2 = 42° and angle 3 = 113° .
In the question ,
a figure is given ,
the labelled diagram is show below .
we can see that the angle ACB and angle ECD are vertically opposite angles ,
we know that, the vertically opposite angles are equal ,
So, angle ACB = m∠2 = 42°
In triangle ABC
By Angle Sum Property Of Triangle ,
angle A + angle B [tex]+[/tex] angle C [tex]=[/tex] 180°
50° + m∠1 + 42° [tex]=[/tex] 180°
92° + m∠1 = 180°
m∠1 = 180° - 92°
m∠1 = 88°
In triangle CDE ,
By Angle Sum Property Of Triangle
angle C + angle D [tex]+[/tex] angle E [tex]=[/tex] 180°
42° + m∠3 + 25° [tex]=[/tex] 180°
m∠3 + 67° = 180°
m∠3 = 180° - 67°
m∠3 = 113°
Therefore , The measure of angle 1 = 88°, angle 2 = 42° and angle 3 = 113° .
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Joel types 180 words in 4 minutes.
How many words per minute
can he type?
Answer:
45 words
Hope this helps :)
Step-by-step explanation:
We know that he can type 180 wprds in 4 minutes.
So to find how man words he types per minute which is 1 minute, then we need to divide 180 by 4.
1. Divide.
45
4| 180
- 16↓
20
- 20
0
2. Answer.
Joel can type 45 words per minute.
3. Check.
45
× 4
180 ✓
Which expression is a difference of a number and a product?
OA. 7-5x
OB. 5+x-3
C. 5(x-3)
OD. 3+5x
⇒Option A is an expression of a difference 7 and 5x which is the product of 5 and x.
⇒Option A is the answer.
the car owner decided to test this by tracking 30 trips. the average mpg the car owner achieved was 24.1 mpg with a standard deviation of 2.1. flag question: question 9 question 92 pts what is the lower estimate (limit) of the 95% confidence interval for the average miles per gallon? (report to 2 decimal places)
The lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.
How to calculate the lower limit of the confidence interval?
Given,
n = 30
mean = μ = 24.1
standard deviation = σ = 2.1
confidence interval = 95%
Since the sample is 30, use t-table. If sample is greater than 30 use z-table.
Level of significance, α = 1 - 0.95 = 0.05
degree of freedom, df = n - 1 = 30 - 1 = 29
t value = 2.045
Lower limit = [tex]\mu-t\frac{s}{\sqrt{n}}[/tex]
= [tex]24.1 - 2.045\frac{2.1}{\sqrt{30}}[/tex]
= 24.1 - 0.784
= 23.316
= 23.32 mpg
Thus, the lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.
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A web designer charges a $200 fee plus $50 per hour to build a website. Which equation represents the total cost, y, to a customer based on the number of hours, x, it takes to buld the website?
Answer: 50x+200=y
Step-by-step explanation:
This is the answer because the number of hours is not provided leaving us to multiply 50 by x, 200 is the flat fee so we will know to automatically add that to our first step and since y is the total this will form the equation, 50x+200=y.
In the formula A = r², find A when ris
14 centimeters.
Step-by-step explanation:
A = r², find A when r is 14 centimeters.
A = (14)²
A = 196 cm²
Which triangles can be mapped onto one another through a sequence of rigid transformations
Answer:
e and c
Step-by-step explanation:
both are the exact same size, which would allow them to be placed on top of each other without any overlap
Answer:
A, B and E are the correct answers
Step-by-step explanation:
I had that same question on the test too.
calculate the surface area of box A 6in 6in 7in box B 3in 8in 9in
The surface area of box A is 240in².
the surface area of box B is 246in².
What is Surface area?
This is referred to as the space/ area occupied by a three- dimensional object by its outer, flat surface of an object.
Formular for calculating surface area is:
Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)
where
Length, L
Height,H
Width,W
from the Question box A
L= 6in
W= 6in
H= 7in
Hence
Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)
=( 2*6*6)+( 2*6*7) +=( 2*6*7)
=72+84+84
= 240in².
from the Question box B
L= 3in
W= 8in
H= 9in
Hence
Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)
=( 2*3*8)+( 2*3*9) +=( 2*8*9)
=48+54+144
= 246in².
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Find the equation of the line passing through the given point and parallel to the given line.
( -1 , -1 ), x + y = 8
( -5 , -2), y + 3x = 10
The equation of the line that passes through (-1, -1) and is parallel to x + y = 8 is x + y = -2
The equation of the line that passes through (-5, -2) and is parallel to y + 3x = 10 is 3x + y = -17
Equation of a lineFrom the question, we are to determine the equation of the line passing through the given points and parallel to the given line.
NOTE: If two lines are parallel, then their slopes are equal
First, we will determine the slopes of the given line
x + y = 8
Write the equation in the slope-intercept form, y = mx + b
Where m is the slope
and b is the y-intercept
x + y = 8 becomes
y = -x + 8
Therefore, m = -1
Now, we will determine the equation of a line that has a slope of -1 and that passes through (-1, -1)
Using the point-slope form of the equation of a straight line,
y - y₁ = m(x - x₁)
y - (-1) = -1(x - (-1))
y + 1 = -1(x + 1)
y + 1 = -x -1
x + y = -1 -1
x + y = -2
Hence, the equation is x + y = -2
Now, we will determine the slope of y + 3x = 10
Express the equation in slope-intercept form
y + 3x = 10
y = -3x + 10
Therefore, m = -3
Now, we will determine the equation of a line that has a slope of -3 and that passes through (-5, -2)
Using the point-slope form of the equation of a straight line,
y - y₁ = m(x - x₁)
y - (-2) = -3(x - (-5))
y + 2 = -3(x + 5)
y + 2 = -3x - 15
3x + y = -15 -2
3x + y = -17
Hence, the equation is 3x + y = -17
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One fifth of a number plus three times the number is equal to twice the number plus 42 . What is the number
The value of the number is 35
What are algebraic expression?Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.These letters are called variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
If the number is represented by x then,
1x/5+3x= 2x+42
making the left hand side a single fraction, then,
(x+15x)/5= 2x+42
16x/5= 2x+42
multiply both sides by 5
16x= 10x+210
collect like terms
16x-10x= 210
6x= 210
x=35
therefore the value of the number is 35
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The perimeter of a rectangle is 150 inches. The width is 12 inches. Find the length.
Answer:
63 inches
Step-by-step explanation:
The perimeter of a rectangle is found by adding all of the side lengths. Since both pairs of opposite sides have the same length, an equation for the perimeter can be written like this:
[tex]P=2w+2l[/tex]
Where w and l represent the width and length.
Since we are asked to find the length, rewrite the equation in terms of l:
[tex]l=\frac{P-2w}{2}[/tex]
We know the values for P and w, so plug those in:
[tex]l=\frac{150-2(12)}{2}[/tex]
Now simplify!
[tex]l=\frac{126}{2}=63[/tex]
Answer:
l = 63 in
Step-by-step explanation: If the P=150 in W=12 in so .... using the formula P=2 (l + w) you get L= P/2 - W = 150/2 - 12 = 63 in. I hope this helps!