3.45g + 2.41q = 50
Explanations:Price of one gallon of gas = $3.45
Price of one quart of oil = $2.41
Number of gallons of gas bought = g
Number of quarts of oil bought = q
Total amount spent = $50
Total amount of gas bought = (Price of one gallon of gas) x (Number of gallons of gas bought)
Total amount of gas bought = 3.45g
Total amount of oil bought = (Price of one quart of oil) x (Number of quarts of oil bought)
Total amount of oil bought = 2.41q
Total amount of gas bought + Total amount of oil bought = Total amount spent
3.45g + 2.41q = 50
Therefore, the required equation is:
3.45g + 2.41q = 50
If y=mx, and y is 12 when x is 4, then what is the constant of proportionality in this equation?A. 1/3B. 3C. 8D. 16
The constant of proportionality,m, is 3 (option B)
Helen carns $14.75 per hour as a babysitter. She recolvos timo-and-a-half pay for any hours sho works over 40 in a wook. What are hor wages in a wook in which showоrkеd 60 hours?$798.05$811.30$821,70$832.65None of those choices are correct
Given data:
The given earning per hour is E=$14.75.
The expression for the money for 50 hours is,
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The coefficients in the expansion of (x+y)6 are?
Answer:
1, 6, 15, 20, 15, 6, 1
Explanation:
Given the expression
(x+y)^6
To determine the coefficient of the expansion, we will use the pascal triangle as shown:
For degree 0, coefficeint is 1
For degree 1, coefficeint is 1, 1
For degree 2, coefficeints are 1, 2, 1
For degree 3, coefficeints are 1, 3, 3, 1
For degree 4, coefficeints are 1, 4, 6, 4, 1
For degree 5, coefficeints are 1, 5, 10, 10, 5, 1
For degree 6, coefficeints are 1, 6, 15, 20,15, 6, 1
Hence the coefficients in the expansion are 1, 6, 15, 20,15, 6, 1
The table gives the temperature (in F) in five cities at 6 a.m. on the same day. Use the table to answer the questions CityTemperature(F)Buffalo-6Dayton48Atlanta64Winnipeg -16Juneau-26(a)How much higher was the 6a.m. temperature in Dayton than in Buffalo?(b)By noon, the temperature in Juneau had risen by 13F .What was the temperature there at noon?
Solution
Question A:
- The Buffalo temperature was -6° F and the temperature at Dayton was 48° F.
- Thus, we can find how much more the temperature in Dayton is compared to the temperature at Buffalo by subtracting both temperatures. That is,
[tex]\begin{gathered} \text{ Temperature in Dayton - Temperature in Buffalo} \\ 48°F-(-6°F)=48°F+6°F=54°F \end{gathered}[/tex]- The temperature at Dayton is 54° F higher than the temperature in Buffalo.
Question B:
- The noon temperature in Juneau has increased by 13℉ by noon. This implies that we should add this increase in temperature to the initial temperature in Juneau when it was 6 am.
- This is done below:
[tex]\begin{gathered} \text{ Juneau temperature by noon is} \\ -26℉+13℉=-13℉ \end{gathered}[/tex]- The temperature in Juneau at noon is -13℉
Final Answer
- The temperature at Dayton is 54° F higher than the temperature in Buffalo.
- The temperature in Juneau at noon is -13℉
Hello could you please help me with question number six?
Given:
Camilo purchased a coin from the dealer for $300.
Value of the coin increases 5% per year.
[tex]\begin{gathered} \text{Value of the coin in 5 years=}300(1+\frac{5}{100})^5 \\ \text{Value of the coin in 5 years=}300(\frac{105}{100})^5 \\ \text{Value of the coin in 5 years=}300(1.2763) \\ \text{Value of the coin in 5 years= \$382.}89 \end{gathered}[/tex]4.) A survey is measuring the distanc3 across a river. He sets up two similar right triangles and finds that DE=2.4 meters and CD=7 meters. If A (<-triangle) EDC, then what is AB?A.) 7.2 MB.) 12 MC.) 15 MD.) 25 M5.) Which of the following statements is true, if parallelogram ABCD is similar to parallelogram PQRS in this truss bridge?A.) m
If ABCD is similar to PQRS then the corresponding angles are congruent. In this case, of the given options there is only one that says that 2 corresponding angles are congruent. This option is m
Ali Ben and Carla made a total of 20 sandwiches ben made three times as many ali and Carla made twice as many as Ben how many sandwiches did Ali make?
We know that
• They made 20 sandwiches in total.
,• Ben made three times as many as Ali made.
,• Carla made twice as many as Ben.
Let's call Ben, Ali, and Carla B, A, and C.
The first statement would be expressed as
[tex]A+B+C=20[/tex]The second statement would be
[tex]B=3A[/tex]The third statement would be
[tex]C=2B[/tex]We have to find an equation with variable A only. Let's replace the second equation in the first one.
[tex]A+3A+C=20[/tex]Then, we replace the second equation with the third one.
[tex]C=2(3A)=6A[/tex]This last expression we include in the total sum to express it as A.
[tex]A+3A+6A=20[/tex]Then, we solve for A.
[tex]\begin{gathered} 10A=20 \\ A=\frac{20}{10} \\ A=2 \end{gathered}[/tex]Therefore, Ali made 2 sandwiches.Find the deviations from the mean for the set of data: 27, 30, 23, 25, 25.Score2730232525Deviation means for the set of data
The mean deviation for the set of data = 2
Explanation:The given set of data is:
27, 30, 23, 25, 25.
The mean deviation formula for ungrouped data is:
[tex]MD=\frac{\sum_^|x-\mu|}{n}[/tex]The sample size, n = 5
The mean, µ = (27 + 30 + 23 + 25 + 25)/5
µ = 130/5
µ = 26
[tex]\begin{gathered} \sum_^|x-\mu|=|27-26|+|30-26|+|23-26|+|25-26|+|25-26| \\ \\ \sum_^|x-\mu|=|1|+|4|+|-3|+|-1|+|-1| \\ \\ \sum_^|x-\mu|=1+4+3+1+1 \\ \\ \sum_^|x-\mu|=10 \end{gathered}[/tex]The mean deviation is therefore:
[tex]\begin{gathered} MD=\frac{\sum_^|x-\mu|}{n} \\ \\ MD=\frac{10}{5} \\ \\ MD=2 \end{gathered}[/tex]The mean deviation for the set of data = 2
What is the area of the polygon A)96 cm2B)64 cm2C)256 cm2D)112 cm2
Answer:
64 cm^2
Step-by-step explanation:
Area of the square is: 4*4 = 16
Area of one triangle on star: 0.5*4*6 = 12
Area of all 4 triangles: 12*4 = 48
Total area: 16 + 48 = 64
Need help solving these problems, work being shown is needed also
Let's start by solving for side y using trigonometric ratios, specifically cosine.
[tex]cos(30)=\frac{y}{8}[/tex]We can solve for y by multiplying 8 to both sides of the equation.
[tex]y=6.9282[/tex]Let's solve for side x using trigonometric ratios, and this time we'll be using sine.
[tex]sin(30)=\frac{x}{8}[/tex]Multiply both sides of the equation by 8.
[tex]x=4[/tex]We have solved for the missing variables x and y:
x = 4 and y = 6.9
Avionna earns $24.44/h and works 32 hours per week. What is her gross annualincome? Round answer to the hundredths place. IF answer does not havehundredths place then use zero so that it does. Use the word for the units not asymbol.
Avionna earns $24.44/h
She works 32 hours per week, the amount she earns per week will be
[tex]=24.44\times32=\text{ \$782.08}[/tex]To calculate her annualm gross income, we multiply by 52 (number of weeks in a year?
Her annual gross income will be
[tex]\begin{gathered} =782.08\times52 \\ =\text{ \$40668.16} \end{gathered}[/tex]Hence her gross annual income is $40668.16 (nearest hundredth)
john lives 3/8 mile from the museum of science. sylvia lives 1/4 mile from the museum of science. how much closer is sylvia to the museum?
We have that the distance Sylvia is closer to the museum equals:
[tex]\frac{3}{8}-\frac{1}{4}=\frac{1}{8}=0.125[/tex]So, she is 0.125 miles closer than John.
***
To determine the difference between two values, we subtract the smallest value from the greatest value, which gives us the difference between them.
Since 3/8 > 1/4 we subtract 1/4 from 3/8.
the form y=axPlot five points on the graph of the function: one point with x=graph-a-function button.10130141
At first let us choose the 5 points
at x = 0, y = 0
The first point is (0, 0)
[tex]y=ax^3[/tex]We will choose a = 1/2
The points are
(-2, -4)
(-1, -1/2)
(0, 0)
(1, 1/2)
(2, 4)
[tex]y=\frac{1}{2}^{}x^3[/tex]13. A florist uses 56 roses to make 4 identicalfloral arrangements. At this rate, how manyroses would the Florist use to create 36identical arrangements?Record your answer. Be sure to use thecorrect place value.0000.00+/-
Answer:
504 roses
Explanation:
[tex]\begin{gathered} 4\text{ identical arrangement are made using 56 roses} \\ 1\text{ identical arrangement is made using }\frac{\text{56}}{4}=14\text{ roses} \\ \text{Therefore:} \\ 36\text{ identical arrangement are made using 36}\times14=504\text{ roses} \end{gathered}[/tex]4. What is the average rate of change of the function over5. Write an exponential function of the form y=abto represent the table below.(1,2),(2,8),(3,32),(4,128) with
PROBLEM
Function
Table
[tex]\begin{gathered} \text{Rate of change = }\frac{y_{2\text{ }}-y_1}{x_2-x_1} \\ \end{gathered}[/tex]
y =
If the probability of an event A occurring is 0.629, what is the complement of A?
Answer:
[tex]P(A^{\prime})\text{ = 0.371}[/tex]
Explanation:
Here, we want to find the complement of A
To find this, we know that the sum of the probability of an event and its complement is 1
Thus, mathematically, we have it that:
[tex]P(A)\text{ + P(A') = 1}[/tex]We have this as:
[tex]\begin{gathered} P(A^{\prime})\text{ = 1-P(A)} \\ P(A^{\prime})\text{ = 1-0.629} \\ P(A^{\prime})\text{ = 0.371} \end{gathered}[/tex]a 16 foot piece of wood was cut into two pieces. the longer of is 3 feet less than twice the shorter piece. what is the length of the longer piece of wood?
Explanation
Step 1
Let
total length(purple line)= 16 feet
shorter piece= x
twice the shorter piece=2x
the longer piece= y
the longer is 3 feet less than twice the shorter piece.( in other words you have to add 3 to the longer pice to obtain twice the shorter piece)
[tex]\begin{gathered} y+3=2x \\ y=2x-3\text{ Equation (1)} \end{gathered}[/tex]Also
shorter piece+longer piece = full wood piece
replacing
[tex]x+y=16\text{ Equation (2)}[/tex]Step 2
fin x and y , using Equation (1) and (2)
i)repace equation (1) in equation (2)
[tex]\begin{gathered} y=2x-3\text{ Equation (1)} \\ x+y=16\text{ Equation (2)} \\ repplace \\ x+2x-3=16 \\ 3x-3=16 \\ 3x=16+3 \\ x=\frac{19}{3} \end{gathered}[/tex]ii)
replace the value of x in equation (1) to find y
[tex]\begin{gathered} y=2x-3\text{ Equation (1)} \\ y=2\cdot\frac{19}{3}-3 \\ y=\frac{38}{3}-3 \\ y=\frac{29}{3} \end{gathered}[/tex]I hope this helps you
I need step by step help understanding dividing decimals the question is 0.86 divided by 0.004
Here are the steps in dividing the given decimal.
1. Convert the divisor 0.004 into a non-decimal value by multiplying it by 1000.
[tex]0.004\times1000=4[/tex]In the same way, multiply the dividend 0.86 by 1000 as well.
[tex]0.86\times1000=860[/tex]2. The division now becomes 860 divided by 4. Let's now divide the numbers using short division.
Hence, the quotient of 860 by 4 is 215.
Therefore, 0.86 divided by 0.004 is 215.
Answer:
215.
Step-by-step explanation:
Divide decimals by multiplying both numbers by a factor of 10 so the divisor no longer has a decimal value. Then, use long division to divide as normal. Place the decimal point in the quotient directly above the decimal point in the dividend. Multiply both by 100 to get rid of the decimal part in the divisor.
This question makes no sense to me at all.Take a look and maybe you could help
Taking two of the exact points:
[tex]\begin{gathered} (x1,y1)=(2,50) \\ (x2,y2)=(6,80) \\ m=\frac{y2-y1}{x2-x1}=\frac{80-50}{6-2}=\frac{30}{4}=7.5 \\ \end{gathered}[/tex]From the graph we can also conclude that the y-intercept could be 45, therefore the function which best models that data is:
[tex]y=6.52x+45[/tex]On a graph the point is (2,2) is it enough information to plot if yes what's the equation of it if not say no
To plot a point on a graph, you need the x and y coordinates.
In this case, the x-coordinate is 2 and the y-coordinate is 2 thus you can plot
(2,2) on a graph.
To get the equation of a line, you need the slope m of the line, a point and another imaginary point (x,y). So in this question you still need the slope to find the equation.
The equation is : No
Answer
1. The point can be plotted on a graph
2. No, the equation can not be determined because the gradient is not known.
2 2 -2 Which of the following is an equation of line k in the xy-plane above? (A) y=-*-4 (B) y = x+2 (C) 2y - 3x = -8 (D) 2y - 3x = -4
Answer
Option C is correct.
The equation of line k is 2y - 3x = -8
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
From the graph attached, we can see that the y-intercept is -4 because the line crosses the y-axis at (0, -4).
Then, for the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the points where the graph crosses the x and y axis as the two points,
(x₁, y₁) and (x₂, y₂) are (0, -4) and (8/3, 0)
[tex]\text{Slope = }\frac{0-(-4)}{\frac{8}{3}-0}=\frac{4}{\frac{8}{3}}=\frac{3}{2}[/tex]Recall that
y = mx + c
m = 3/2
c = -4
y = (3/2) (x) - 4
Multiply through by 2
2y = 3x - 8
2y - 3x = -8
Hope this Helps!!!
What are the necessary conditions to apply the SAS Triangle Congruence Theorem?
See explanation below
Explanation:The necessary conditions to apply the SAS Triangle Congruence Theorem:
The angle included between any two sides of a triangle must be the same with the corresponding two sides and angle included in another triangle.
SAS = side-angle-sides
From the diagram above, triangle ABC is congruent to triangle EFG under the SAS triangle theorem
In other words, two triangles are congruent if the pair of the sides in each triangle and the included angle are congruent.
10. consecutive 11. alternative exterior 12. alternative interiorI need help with explanation why that's the answer
3 and 4 are consecutive: when two lines are crossed by another line calledtransversal.
ABC and GFH are alternate exterior: are a pair of angles on the outer side of each of those lines but on opposite sides of the transversal.
. and . are alternate interior. are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
A community college employs 87 full-time faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 87
Using the provided random number table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row 3, column 6. Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample.
The numbers for the faculty members are
enter your response here.
(Use a comma to separate answers as needed.)
4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9 are the numbers that would make up the sample.
The entire inquiry is included as an attachment.
The parameters are as follows:
3 rows and 6 columns.
How can the number that will be in the sample be determined?
The entire inquiry is included as an attachment.
The parameters are as follows:
3 rows and 6 columns.
The entries in row 3 of the attached figure are as follows: 4, 1, 1, 4, 7, 9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7. 1
The entries in column 6 of the attached figure are: 1, 6, 9, 5, 4, 9.
Consequently, the sample would contain the following numbers: 4, 1, 1, 4, 7,9, 2, 6, 4, 7, 4, 4, 1, 0, 3, 0, 5, 0, 7, 1, 1, 6, 5, 4, 9
To learn more about the problem refer to:
https://brainly.com/question/28170431
#SPJ1
Solve the triangle: a=63, =93,6=83. If it is not possible, say so.This triangle is not solvable.a=77.8.8= 60.7.y=41.5=41.5.6=77.8.y=60.7a = 607.6= 415.y=77.8
It is given that
[tex]a=6.3,b=9.3,c=8.3[/tex]Use the cosine rule to get:
[tex]\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc}=\frac{(9.3)^2+(8.3)^2-(6.3)^2}{2\ast9.3\ast8.3}=0.7493 \\ A=\cos ^{-1}(0.7493)=41.46\approx41.5^{\circ} \end{gathered}[/tex]Similarly for angle B it follows:
[tex]\begin{gathered} \cos B=\frac{a^2+c^2-b^2}{2ac}=\frac{(6.3)^2+(8.3)^2-(9.3)^2}{2\ast6.3\ast8.3}=\frac{2209}{10458} \\ B=\cos ^{-1}(\frac{2209}{10458})=77.8^{\circ} \end{gathered}[/tex]The value for angle C is given by the formula
[tex]\begin{gathered} A+B+C=180 \\ C=180-B-A \\ C=180-77.8-41.5=60.7^{\circ} \end{gathered}[/tex]Hence option C is correct.
Karla says 4 2/3 and 4.7 would fall between ✓17 and 4 3/4O FactO Fib
As we can see:
4.66666.... is between 4.1231.... and 4.75
And
4.7 is also between 4.1231... and 4.75.
Therefore, it is a fact.
Please help me with the second one what is the average rate of change?
It's important to know that the domain refers to the x-values of the function, and the range refers to the y-values of the function. Graphically, the domain would be the x-axis and the range would be the y-axis, that is, their values.
As you can observe in the given graph, the function doesn't have any interruption or restriction horizontally, it goes from the negative x-axis to the positive x-axis, this means the domain is all real numbers from negative infinity to positive infinity, as follows
[tex]D=(-\infty,\infty)[/tex]On the other hand, the range of the given function is from y = -2 to positive infinity, it's important to know that y = -2 is excluded from the range because as you can observe the function curves there without crossing y = -2. So, the range is
[tex]R=(-2,\infty)[/tex]For the second question of the problem, we have to select two y-values from x = 0 and x = 1, which is the given interval. From the graph, we can identify that x = 0 belongs to y = -1, and x = 1 belongs to y = 1. So, we have the points (0,-1) and (1,1). Now, we use the following formula to find the average rate of change.
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where a = 0, f(a) = -1, b = 1, and f(b) = 1, note that these values are the coordinates of the two points we selected. Let's use these values to find the rate.
[tex]r=\frac{1-(-1)}{1-0}=\frac{1+1}{1}=\frac{2}{1}=2[/tex]Therefore, the average rate of change over the interval [1,0] is 2.Answer:
the average rate of change over the interval [1,0] is 2.
Step-by-step explanation:
A student was asked to rewrite using only the associative property of multiplication. Which is the correct response?
Given that the associative property of multiplication says that you can group the numbers in any combination, we can reorganize the expression as: 7·(10·3)=210. So the answer would be the first option.
A backpack is on sale for 25% off after the discount is taken a 7% sales tax is apply if original price of the backpack is P which equation represents the final cost C in dollars of the backpack
c = p(0.75)(1.07)
Explanation:The original price of the backpack = p
Discount = 25%
Percentage paid = 100% - 25% = 75%
Discounted price = 75% of p
Discounted price = 75/100 x p
Discounted price = 0.75p
Sales tax = 7% of 0.75p
Final cost = 107% of 0.75p
Final cost = (107/100) x 0.75p
Final cost = (1.07)(0.75)(p)
c = p(0.75)(1.07)
How many 3/4 cup servings can be made if there is 7/8 of a cup of broccoli in a bowl
They can be made the following number of 3/4 cup servings:
[tex]\frac{7}{8}(\frac{3}{4})=\frac{21}{32}\approx0.7[/tex]So, they can make approximately 0.7 servings