A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.
The problem can be solved using the average value approach.
Average value = total amount or sum of data / number of data
In the given problem,
total amount = total coffee served last year
total amount = 40,000
number of data = number of hours in a year
number of data = 365 day/year x 24 hours/day = 8760 hours
Hence,
Average value = total amount or sum of data / number of data
= 40000 / 8760
= 4,6 ≈ 5 (round to the nearest whole cup)
Hence, the average coffee served is 5 cups per hour.
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Write an equation of a line in slope intercept form with a slope of 3/2 that passes through point (4,7).
Answer:
y
=
−
3
2
x
+
13
Explanation:
First write it using point-slope form:
y
−
7
=
−
3
2
(
x
−
4
)
Now simplify to slope-intercept:
Add 7 to each side:
y
=
−
3
2
(
x
−
4
)
+
7
Distribute
−
3
2
to each term in the parentheses:
y
=
−
3
2
x
+
6
+
7
y
=
−
3
2
x
+
13
hope I helped you:)
Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve.
If y = 21 when x = 14, find y when x = 40 .
ur answer should have ,60
Answer:
see explanation
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 21 when x = 14 , then
21 = 14k ( divide both sides by 14 )
[tex]\frac{21}{14}[/tex] = k , that is
k = [tex]\frac{3}{2}[/tex] = 1.5
y = 1.5x ← equation of variation
when x = 40 , then
y = 1.5 × 40 = 60
Write an equation for the line parallel to the given line that contains C.
C(1,5); y= -4x+7
Answer:
y=-4x+9
Step-by-step explanation:
We will find an equation in the form of y = mx + b. We know m must be -4(because the slope must be the same for parallel lines), so we need to solve for b, which is the y-intercept. To do that, we will plug in the point C, giving us [tex]5 = -4 * 1 + b[/tex]. Adding 4 to both sides gives us b = 9, so that is the y-intercept.
What is the value of x?
Answer: 2
Step-by-step explanation:
Since both triangles are similar you can set both side lengths to be equal
4x = 16x -24
Isolate x on one side
-12x = -24
Then solve for x
x = 2
in a regression analysis, a(n) is used to predict a(n) . a. ordinal variable, ratio variable b. independent variable, dependent variable c. nominal variable, independent variable d. response variable, explanatory variable
In a regression analysis, a(n) is used to predict a(n) is known as option (b).independent variable, dependent variable.
Regression analysis:
In the concept of statistics, the regression analysis is useful to come up with a predictive model consisting of dependent and independent variables. And the R-squared value for a regression equation indicates the percentage of variability in the dependent variable being expressed by the variability in the independent variables.
Given,
Here we need to find the type of variable for a regression analysis, a(n) is used to predict a(n).
As per the definition of regression analysis, in the given question, we have two variable there are
=> a(n)
After prediction, the predicted value of a(n).
Here the first one is the independent variable because the this value is the based to predict the value of the other one is the dependent variable.
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if the original recipe calls for 50 portions, 6oz each and the new recipe calls for 100 portions at 5oz each, what is the recipe conversion factor?
By using multiplication and division of integers, it can be calculated that
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
What is multiplication and division of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem where multiplication and division of integers is required
The original recipe calls for 50 portions, 6oz each
Required yield of the original recipe = 50 [tex]\times[/tex] 6 = 300 oz
The new recipe calls for 100 portions at 5oz each
Required yield of the new recipe = 100 [tex]\times[/tex] 5 = 500 oz
Conversion factor of the recipe = [tex]\frac{500}{300}[/tex] = 1.6
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Wrote an equation with a vertex : (4,-5)
passes through: (2,-1)
ab³ (5a²-4ab+b²) multiply
Answer: The correct answer is 5a^3b^3 − 4a^2b^4 + ab^5
Step-by-step explanation:
ab^3 (5a^2 − 4ab + b^2)
Multiply together:
(ab^3)*(5a^2 + −4ab + b^2)
(ab^3)*(5a^2) + (ab^3)*(−4ab) + (ab^3)*(b^2)
= 5a^3b^3 − 4a^2b^4 + ab^5
Answer:
[tex]5a^3b^3-4a^2b^4+ab^5[/tex]
Step-by-step explanation:
Given expression:
[tex]ab^3(5a^2-4ab+b^2)[/tex]
Apply the distributive property a(b - c + d) = ab - ac + ad :
[tex]\implies ab^3 \cdot5 a^2-ab^3 \cdot 4ab+ab^3 \cdot b^2[/tex]
Collect like terms:
[tex]\implies 5aa^2b^3-4aabb^3+ab^2b^3[/tex]
Apply the exponent rule a = a¹ :
[tex]\implies 5a^1a^2b^3-4a^1a^1b^1b^3+a^1b^2b^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 5a^{(1+2)}b^3-4a^{(1+1)}b^{(1+3)}+a^1b^{(2+3)}[/tex]
Simplify:
[tex]\implies 5a^3b^3-4a^2b^4+ab^5[/tex]
write the expression as a sum and/or difference of logarithms. express exponents as factors.log5 a3 b
Expression of logarithms is log₅a³b = 3log₅a + log₅b.
Given expression is log₅a³b.
We have to express given expression as a sum or difference of logarithms.
We know the logarithmic formulas which is,
logₐ(PQ) = logₐP + logₐQ
logₐ([tex]P^{Q}[/tex]) = QlogₐP
we will use above formulas and solve the given equation.
log₅a³b = log₅a³ + log₅b
log₅a³b = 3log₅a + log₅b
Logarithms, like exponents, have many helpful properties that can be used to simplify logarithmic expressions ans solve logarithmic equation.
The product property states that to miltiply two powers that have the same base, add the exponents.
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Nancy i making acceorie for the occer team. She ue 566. 28 inche of fabric on headband for 36 player and 3 coache. She alo ue 306. 36 inche of fabric on writband for jut the player. How much fabric wa ued on a headband and writband for each player?
Using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.
So, given that we've done it:
There are 35 players.
There are two coaches.
The cloth on the headbands measures 598.66 inches in length.
Just for the players, the wristbands include 302.05 inches of fabric.
Each player's headband's fabric length is specified by:
= Total inches/Total number of persons
= 598.66/37
= 16.18 inches
Each player's wristband's fabric length is specified by:
= Total inches/Number of persons
= 302.05/35
= 8.63 inches
Therefore, using some mathematical operations, we know that each player's headband and wristband are made from 16.18 inches of fabric and 8.63 inches of fabric.
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Complete question:
Nancy is making accessories for the soccer team. She uses 598.66 inches of fabric on headbands for 35 players and 2 coaches. She also uses 302.05 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
f(x) = 2x²+ 3x - 14.
Answer:
Step-by-step explanation:
domain = all real numbers
range = {-121/8,∞)x-intercepts (2,0)
y-intercepts (0,-14)
vertex = minimum (-3/1 - 121/8)
Answer: Okay so I got,
1) x intercept = (2, 0), (-7/2, 0) and y intercept (0, -14)
2) 'x' equals to..
-Exact Form: 2, -7/2
-Decimal Form: 2, -3.5
Hope this helps!
Victoria deposited $15,000 into a savings account that earns an annual simple interest rate of 0.2% to the nearest 10th of a year how long will it take for the account to reach 15,500
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
sus
It will take about 16.7 years to reach $15500.
What is the interest rate?The percentage that a lender adds to the amount of money lent to them is called an interest rate.
Given that, the initial deposited amount is P = $15000, the interest rate is r= 0.2% annually, and the final amount is $15500.
The interest earned is calculated by subtracting the initial amount from the final amount:
15500-15000
=500
Therefore, the interest earned is $500.
Now, the formula for the simple interest is:
interest = P × r × t
Substitute the known values:
500 = 15000 × 0.2% × t
500 = 15000 × 0.2/100 ×t
500 = 30t
t = 500/30
t = 16.7
Hence, It will take about 16.7 years to reach $15500.
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If line segment AB represents 50%, what is the length of a line segment that is 100%?
Answer:
it would be CD or 50%
Step-by-step explanation:
suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. random samples of batteries are taken for each brand and the following data are recorded: sample 1: n1
The test statistic of two brands of batteries is -2.177.
How to calculate test statistic?[tex]n_1[/tex] = size of sample 1 = 16
[tex]n_2[/tex] = size of sample 2 = 21
[tex]\bar{x_1}[/tex] = mean of sample 1 = 210
[tex]\bar{x_2}[/tex] = mean of sample 2 = 225
[tex]\sigma_{1}[/tex] = standard deviation of sample 1 = 20
[tex]\sigma_{2}[/tex] = standard deviation of sample 2 = 23
T test is test for statistical hypothesis that follows t-distribution table under null hypothesis. T test is used when test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. So, for this case we use t test for test statistic,
t = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}}[/tex]
t = [tex]\frac{210-225}{\sqrt{\frac{20^2}{16}+\frac{23^2}{21}}}[/tex]
t = [tex]\frac{-15}{\sqrt{\frac{400}{16}+\frac{529}{21}}}[/tex]
t = -15 / 7.0845
t = -2.117
Thus, the two brands of batteries have test statistic result is -2.117
Your question is incomplete, but most probably your full question was
Suppose you are testing to see if there is a difference in population mean lifetime of two brands (1,2) of batteries. Random samples of batteries are taken for each brand and the following data are recorded:
Sample 1: n1= 16, X1 = 210, s1= 20
Sample 2: n2= 21, X2 = 225, s2= 23
What is the test statistic assuming unequal population standard deviations?
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a shipment of 15 televisions contains 6 regular and 9 deluxe models. the manufacturer failed to mark the model designation on the cartons. if 3 cartons are selected at random, what is the probability that exactly 2 of them are the deluxe model? (round your answer to three decimal places.)
The probability that exactly 2 of them are the deluxe model =0.474
given that
there is a shipment of 15 televisions contains 6 regular and 9 deluxe models
now 3 cartons are selected at random
C(15,3) =[tex]\frac{15!}{(15-3)!3!}[/tex]
C(15,3) = [tex]\frac{13*14*15}{3*2*1}[/tex]
C(15,3) = 455
2 out of 9 deluxe models be picked
C(9,2) = [tex]\frac{9!}{(9-2)!2!}[/tex]
C(9,2) = [tex]\frac{8*9}{2*1}[/tex]
C(9,2) = 36
Each of these can be matched with 1 of 6 regular models
36 × 6 = 216
the probability that exactly 2 of them are the deluxe model
= [tex]\frac{216}{455}[/tex]
=0.474
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A baker makes a cake that requires 44 ounces of ingredients. The ratio of flour to sugar is 6:5. She didn’t like how the cake tasted so for the new cake, she changed the flour to sugar ratio to 7:6. If the amount of ounces she used increased to 91, how many more ounces of sugar did she add to the new cake? ( BE FAST PLEASE)
The amount of ounces of sugar she added to the new cake is 22 ounces
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the total ounces of ingredients in the cake be = 44 ounces
The ratio of flour to sugar is = 6 : 5
So , the amount of flour in 44 ounces = 6x
The amount of sugar in 44 ounces = 5x
And , the equation is
6x + 5x = 44
On simplifying the equation , we get
11x = 44
Divide by 11 on both sides , we get
x = 4
So , the total amount of sugar in 44 ounces of ingredients = 5x
Substitute the value for x = 4 , we get
Total amount of sugar in 44 ounces of ingredients = 20 ounces
And ,
Let the total ounces of ingredients in the new cake be = 91 ounces
The ratio of flour to sugar is = 7 : 6
So , the amount of flour in 91 ounces = 7y
The amount of sugar in 91 ounces = 6y
And , the equation is
7y + 6y = 91
On simplifying the equation , we get
13y = 91
Divide by 13 on both sides , we get
y = 7
So , the total amount of sugar in 91 ounces of ingredients = 6y
Substitute the value for y = 7 , we get
Total amount of sugar in 91 ounces of ingredients = 42 ounces
Therefore , the extra ounces of sugar the baker added to the new cake is =
Total amount of sugar in 91 ounces of ingredients - Total amount of sugar in 44 ounces of ingredients
The extra ounces of sugar the baker added to the new cake is = 42 - 20
Extra ounces of sugar the baker added to the new cake is = 22 ounces
Hence ,
The amount of ounces of sugar she added to the new cake is 22 ounces
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Anyone know this? Kind of struggling.
Answer:
It's -5 + 3 basicaly because 2 negatives is one positive. So the answer is -2.
Colorful wool is being woven into a scarf in cold, damp Ireland. Wool is used for scarves, sweaters, hats, and gloves because it is a good insulator. If wool is a good insulator, what substance would be a good conductor?
A plastic
B fur
C cotton
D metal
If the nth term of a number sequence is n^2 + 2n,
find the first 3 terms and the 10th term.
Answer:
3, 8, 15 and 120
Step-by-step explanation:
to find the first 3 terms, substitute n = 1, 2, 3 into the nth term rule
n = 1 : 1² + 2(1) = 1 + 2 = 3
n = 2 : 2² + 2(2) = 4 + 4 = 8
n = 3 : 3² + 2(3) = 9 + 6 = 15
the first 3 terms are 3, 8, 15
to find the 10th term , substitute n = 10 into the rule
n = 10 : 10² + 2(10) = 100 + 20 = 120
evaluate the summation for the indicated value of the variable. 1(1!) 2(2!) 3(3!) 4(4!) m(m!); m
The sum of the indicated variable is 23.
What is variable?
A variable is an alphabet or term that represents an unknown variety or unknown worth or unknown amount. The variables are specially employed in the case of pure mathematics expression or pure mathematics.
MAIN body:
the correct expression is as follows :
1(1!) +2(2!) +3(3!)+ 4(4!) ........+ m(m!) where m = 3
for m= 3
the expression becomes:
=1(1!) +2(2!) +3(3!)
factorial means we need to multiply the number until it reaches 1.
= 1*1 + 2*2*1 + 3*3*2*1
= 1+ 4+ 18
= 23
Hence the sum of expression is 23.
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4. Identify each of the following polygons:
Answer:
Step-by-step explanation:
1. Square
2. Rhombus
3. Trapezoid
4. Diamond
5. Octogon
6. Triangle
7. Pentagon
8. Hexagon
9. Triangle?
Use the grid to help you fill in the blank.
0.9 × ___ = 0.27
Answer:
0.3
Step-by-step explanation:
0.9 times 0.3 equals 0.27
$$1,2,2,4,8,32,256,\ldots,$$each term (starting from the third term) is the product of the two terms before it. for example, the seventh term is $256$, which is the product of the fifth term ($8$) and the sixth term ($32$). this sequence can be continued forever, though the numbers very quickly grow enormous! (for example, the $14^{\text{th}}$ term is close to some estimates of the number of particles in the observable universe.) what is the last digit of the $35^{\text{th}}$ term of the sequence?
The last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
Given that,
Each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it. For instance, the seventh term, which is the sum of the fifth ($8) and sixth ($32) terms, is $256. Though the numbers very rapidly become large, this series can go on indefinitely! In terms of the number of particles in the observable universe, the $14 term, for instance, is close to some estimations.
We have to find what is the final digit of the sequence's $35 term.
We know that,
Remember the Fibonacci sequence, which goes 1, 1, 2, 3, 5, 8, 13, 21..., where each word is the total of the one before it. Continuing the above pattern, if Fn is the n-th Fibonacci number, we would arrive at
aₙ=a₂ˣₙ₋₁a₁ˣₙ₋₂=2ˣₙ₋₁
A periodic series of residues mod 10 is left behind by the sequence of positive powers of 2:
2≡2(mod 10)
2²≡4 (mod 10)
2³≡8 (mod 10)
2⁴≡16 (mod 10)
2⁵≡32 (mod 10)
2⁶≡64 (mod 10)
And so forth; this series of residues has a 4-year period.
The taken mod 4 period is 6:
34≡4 (mod 6)
F₃₄≡3 (mod6)
2³=8
So, the last digit of a₃₅ is 8.
Therefore, the last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
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One angle of a triangle measures 75°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
well, since a triangle has a total of 180° interior angles, that means 180 - 75 = 105 is leftover for the other two remaining angles.
now, they're in a 2 : 5 ratio, well, let's simply divide 105° by (2 + 5) and distribute accordingly.
[tex]2~~ : ~~5\implies 2\cdot \frac{105}{2+5}~~ : ~~5\cdot \frac{105}{2+5}\implies 2\cdot 15~~ : ~~5\cdot 15\implies \text{\LARGE 30~~ : ~~75 }[/tex]
if a cup of diced cucumbers weighs 5.3 ounces, how many pounds of prepped cucumbers will you need for your 140 house salads?
46 pounds of prepped cucumbers are needed for 140 house salads.
It is given that one cup of diced cucumbers weighs 5.3 ounces.
Also, we know that one pound= 16 ounces or 1-ounce measure 1/16 pounds, we can do it in any way.
Thus, firstly, we will convert the ounces into pounds.
thus, 5.3 ounces= 5.3/16 pounds
Now, we need prepped cucumbers for 140 house salads, According to the given question.
thus, pounds needed for 140 house salads= 5.3/16*140
=> 46 pounds (nearly)
Thus, 140 house salads need nearly 46 pounds of cucumbers.
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A given triangle has vertices at (-3,1) (2,4) and (5,-3) . If the triangle were rotated 180 degrees counterclockwise, the new coordinates would be ?
The new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
Define transformations.A function, f, that maps to itself are known as a transformation, or f: X → X. The transformation results in the pre-image X becoming the picture X. This transformation can utilize any operation, or a combination of operations, including translation, rotation, reflection, and dilation.
Given, the triangle vertices (-3, 1) (2, 4), and (5, -3).
When the triangle turned 180 degrees counterclockwise, we must determine the new coordinates;
When we rotate 180 degree counterclockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
Therefore, the new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4), (-5, 3).
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the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km. what is the difference between these distances?
HELPPPPPPPPPPPP ASAP!!!!
The difference between these distances on the Earth is 3.32 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.
The difference will be:
= 4.00x10^4 km - 6.8x10^3 km.
= 3.32 × 10⁴
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6(x−2)=−18
due today
Answer: -1
Step-by-step explanation: 6x-12=-18
+12= +12
------------------
-6/6=-1
if you can notice the difference between 10- and 11-pound weights, which of the following weights could you differentiate from a 100-pound weight?
If we can notice the difference between 10- and 11-pound weight, we can differentiate 110-pound weight from a 100-pound weight.
What is weight?All things close to Earth are constantly subject to the force known as weight. All items are pulled downward toward the Earth's core by the gravity of the planet. On the other hand, weight is a measurement of how much gravity pulls an item downward. The mass of the thing has an impact on this force; the heavier the object, the stronger gravity's pull is. The force of gravity acting on a body is the most typical definition of weight given in introductory physics textbooks. This is sometimes formulated as W = mg, where W is the weight, m is the object's mass, and g is the acceleration due to gravity.
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(2+8) + 10 ^2 +60 divided 10
Answer: 17
Step-by-step explanation:
Answer:
Step-by-step explanation:
116