Answer: The slope-intercept form for this line is y=4x-10
Step-by-step explanation: To begin with the solution of this problem firstly, write down the equation of the line passing through the point (4, 6) with a slope of 4 in slope-intercept form (y = mx + b), now take a look at the following point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is the point (4, 6) and m is the slope of the line, which is 4. now substitute these values in the above equation, we get:
y - 6 = 4(x - 4)
Expanding the right-hand side, we get:
y - 6 = 4x - 16
Adding 6 to both sides, we get:
y = 4x - 10
Therefore, the equation of the line in slope-intercept form is:
y=4x-10
To learn more about slope-intercept form of equation,
https://brainly.com/question/29113319
work out the lengths of sides a and b give your answer to 1dp
The lengths of sides a and b are given as follows:
a = 14.3. b = 24.What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is obtained as follows:
m < B + 81 + 33 = 180
m < B = 180 - 114
m < B = 66º.
Then the relation is:
26/sin(81º) = a/sin(33º) = b/sin(66º).
Then the value of a is obtained as follows:
26/sin(81º) = a/sin(33º)
a = 26 x sine of 33 degrees/sine of 81 degrees
a = 14.3.
The value of b is obtained as follows:
26/sin(81º) = b/sin(66º)
b = 26 x sine of 66 degrees/sine of 81 degrees
b = 24.
Missing InformationThe triangle is given by the image presented at the end of the answer.
More can be learned about the law of sines at https://brainly.com/question/4372174
#SPJ1
Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf.
She writes the expression (x−5)(50−2x)
to represent her profit based on the price per scarf, x
.
Enter Sofie's average change in profit for two different sections of the graph.
A graph has price per scarf (dollars) on the x-axis, and profit (dollars) on the y-axis. A parabola with equation f (x) = (x minus 5) (50 minus 2 x) opens down and goes through (5, 0), has vertex (15, 200), and goes through (25, 0).
CLEAR CHECK
What is Sofie's average change in profit from x=5
to x=15
?
For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.
What is Sofie's average change in profit from x=15
to x=25
?
For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.
3^17 mod 25. Can anyone tell me how they got 6?
17 in binary is 10001.
How to Convert 17 in Binary?
Step 1: Divide 17 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.
Write the remainder from bottom to top i.e. in the reverse chronological order. This will give the binary equivalent of 17.
Therefore, the binary equivalent of decimal number 17 is 10001.
Learn more about binary number click;
https://brainly.com/question/31102086
#SPJ1
A rectangular prisms has a length of 2 1/2 centimeters a width of 2 1/2 centimeters and a height of 5 centimeters Justin has a storage container for the prism that has a volume of 35 cubic centimeters
It could be feasible to accommodate the prism diagonally or by orienting it in a certain way, depending on the geometry of the container.
Given that:
Length, L = 2 and 1/2 = 2.5 cm
Width, W = 2 and 1/2 = 2.5 cm
Height, H = 5 cm
The volume of the rectangular prism is calculated as,
Volume = 2.5 x 2.5 x 5
Volume = 31.25 cubic centimeters
Therefore, the volume of the rectangular prism is 31.25 cubic centimeters.
More about the volume of the rectangular prism link is given below.
https://brainly.com/question/21334693
#SPJ1
Please answer the question
Please help studying for next grade.
93+48÷(12-42)x17
Answer:
65.8
Step-by-step explanation:
to solve such equations u should use (PEMDAS)
parenthesis, exponents, multiplication, division, addition, subtraction
note that multiplication doesn't become always before division if the division is before in the equation we divide then multiply
same with addition and subtraction we add or subtract depnding on what first
other than that we follow the steps i mentioned before
parenthesis, exponents, multiplication, division, addition, subtraction
so solve the parantheses first
then the exponents (you may have not learned this yet)
then multiplication and division together start with the one that comes first
the addition and subtraction start with the one that comes first
so for example :5×5÷5×5
=25÷5×5
=5×5
=25
i started with the first multiplication cuz it came first then division cuz it was before the other multiplication
and then the other multiplication
now here is the answer for your equation 93+48÷(12-42)x17
using PEMDAS(don't write this it's just for explaining)
parantheses first
93+48÷-30×17
we don't have exponents so just skip it
now division and multiplication
93+(-1.6)×17
finally addition amd subtraction
because we don't have subtraction we won't use it too
93 +(-27.2)
=65.8
The length of pregnancy isn't always the same. In pigs, the length of pregnancies varies according to a Normal distribution with mean 114 days and standard deviation 5 days.
What percent of pig pregnancies are longer than 124 days?
In pigs, the length of pregnancies varies according to a Normal distribution with mean 114 days and standard deviation 5 days, approximately 2.28% of pig pregnancies are longer than 124 days.
We can start by standardizing the value 124 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
So in this case:
z = (124 - 114) / 5 = 2
Using a standard normal distribution table or calculator, we can find that the proportion of values greater than 2 is approximately 0.0228.
Therefore, approximately 2.28% of pig pregnancies are longer than 124 days.
For more details regarding standard deviation, visit:
https://brainly.com/question/23907081
#SPJ1
A suitcase weighs 12 kg to the nearest kilogram. Another suitcase weighs 17 kg to the nearest kilogram. Work out the smallest amount, in kilograms (kg), that the two suitcases could weigh in total.
Answer:
28 KG
Step-by-step explanation:
To find the smallest possible weight, we need to consider the possible range of weights for each suitcase based on the rounding.
The 12 kg suitcase could actually weigh anywhere from 11.5 kg to 12.4 kg (since rounding to the nearest kg means it could be as low as 11.5 kg or as high as 12.4 kg, with 12 kg being the nearest whole number).
The 17 kg suitcase could actually weigh anywhere from 16.5 kg to 17.4 kg.
To get the smallest possible total weight, we want to add the lowest weights of each suitcase:
11.5 kg + 16.5 kg = 28 kg
Therefore, the smallest possible amount that the two suitcases could weigh in total is 28 kg.
Answer explication question
The solution is:
The equations are;
4(2x + 5) = 3(2x + 8)
x = 2
Perimeter of each shape is 36
Here, we have,
Mathematically;
The perimeter of a square is 4L
while the perimeter of an equilateral triangle is 3L
where L represents the lengths of the sides
Mathematically, from what we have in the question, since the perimeter are equal;
4(2x + 5) = 3(2x + 8)
8x + 20 = 6x + 24
8x-6x = 24-20
2x = 4
x = 4/2
x = 2
The side of the square will measure;
2(2) + 5 = 9
Its perimeter is 4(9) = 36
The side of the triangle will measure
2(2) + 8 = 12
Its perimeter will be 3(12) = 36
Learn more about perimeter here:
brainly.com/question/397857
#SPJ1
Help!!! I need to fill out this table using logarithm rules and need to do it without a calculator
(The highlighted one is the problem which I need help completing)
Answer:
In the explanation
Hope this helps!
Step-by-step explanation:
1. 20: 1.3010
2. 25: 1.3979
3. 300: 2.4771
4. 500: 2.690 ( 2.6989700 )
5. 8000: 3.9031
6. 0.7: -0.1549
7. 0.04: -1.3979
( The blank for the question on the bottom is pq, refer to the product property in logarithms :) )
Answer:
Step-by-step explanation:
I explain 1 through 10 that should give you an idea of how this goes.
See image for explan
A rectangular pyramid is shown in the figure 5cm 6 cm 4 cm 5.5cm what is the surface area of the pyramid
The total surface area of the square pyramid is 99 cm²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
To get the surface area:
Area of base = 10 cm * 2 cm = 20 cm²
Area of first triangle lateral face = (1/2) * 2 cm * 8 cm = 8 cm²
Area of second triangle lateral face = (1/2) * 10 cm * 6.3 cm = 31.5 cm²
Total surface area = 20 cm² + 2(8 cm²) + 2(31.5 cm²) = 99 cm²
The total surface area is 99 cm²
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Three balls toll at an intervals of
10 minutes, 15 minutes and 20 minutes.
If they toll together all 11:00am.
When next do they toll again?
Next all three balls toll after 60 minutes, that is 12:00 PM.
Given that, Three balls toll at an intervals of 10 minutes, 15 minutes and 20 minutes.
They toll together all 11:00 am.
Take LCM of three different intervals. That is,
10= 2×5
15=3×5
20=2×2×5
So, the LCM is 2×2×3×5= 60
Means all three balls toll after 60 minutes, which is 12:00 PM.
Therefore, next all three balls toll after 60 minutes, that is 12:00 PM.
Learn more about the least common multiple here:
https://brainly.com/question/11533141.
#SPJ1
create a scatterplot for the data in the table. based on the appearance of the scatterplot, which model does the data appear to follow?
a. the data appears to follow a linear model
b. the data appears to follow a quadratic model
c. the data appears to follow a cubic model
d. the data appears to follow an exponential model
Answer:
C. The data appear to follow a cubic model.
Step-by-step explanation:
Plot the points on the graphing calculator, and then generate the best regression model.
For the linear equation, r = -.0529
For the quadratic equation, R^2 = .8992
For the cubic equation, R^2 = .9678
For the exponential equation, r = -.0814
A cubic regression equation would best fit this data. So the correct answer is C.
The ratio of the corresponding linear measures of two similar cans of fruit is 4 to 7. The smaller can has a surface area of 220 square centimeters. Find the surface area of the larger can. Write your answer as a decimal or mixed number.
The surface area is
square centimeters.
The surface area of the larger can is approximately 674.375 square centimeters.
We have,
The ratio of the corresponding linear measures of two similar cans is 4 to 7.
The ratio of their surface areas will be the square of this ratio, which is (4/7)² = 16/49.
Let A be the surface area of the larger can.
(220 cm²) / A = 16/49
220 cm² x 49 = A x 16
10780 cm² = A x 16
A = 10780 cm² / 16
A = 674.375 cm²
Therefore,
The surface area of the larger can is approximately 674.375 square centimeters.
Learn more about the surface area of a can here:
https://brainly.com/question/20505453
#SPJ1
In the triple-jump competition, Lee jumped 28 ft, 32 ft, 29 ft, 30 ft, and
33 ft.
a. Find the mean, median, mode, and range of Lee's marks.
Answer:
• Mean = 30.4
• Median = 30
• Mode = None
• Range = 5
Step-by-step explanation:
To find the mean, we add all the numbers together and divide by the total number of numbers. In this case, we have 5 numbers: 28, 32, 29, 30, and 33. Adding them together gives us 152. Dividing by 5 gives us a mean of 30.4.
To find the median, we need to order the numbers from smallest to largest: 28, 29, 30, 32, and 33. The median is the middle number which is 30.
To find the mode, we look for the number that appears most frequently in the list. In this case, there is no number that appears more than once so there is no mode.
To find the range, we subtract the smallest number from the largest number. In this case, the smallest number is 28 and the largest number is 33 so the range is 5.
Therefore:
• Mean = 30.4
• Median = 30
• Mode = None
• Range = 5
I hope that helps!
x/9=7/15 answer plss
Answer: To solve for x in the equation x/9 = 7/15, we can cross-multiply to get:
15x = 9 * 7
Simplifying the right side, we get:
15x = 63
To solve for x, we can divide both sides by 15:
x = 63/15
Simplifying the fraction on the right side, we get:
x = 4 3/5 or x = 4.2 (rounded to one decimal place)
Therefore, the solution to the equation x/9 = 7/15 is x = 4.2 or x = 4 3/5.
Step-by-step explanation: kinda easy ngl lol but hope this helps :D
If John solved the equation x² - 10x +8=0 by completing the square, one of the steps in his process would
be:
(z-5)² = 17
(z+4)² =10z+16
(z+4)² =10z
(2-5)² = -8
If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.
What is a quadratic equation?In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
x² - 10x + 8 = 0
x² - 10x = -8
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = 8 + (-10/2)²
x² - 10x + 25 = -8 + 25
x² - 10x + 25 = 17
By simplifying, we have;
(x - 5)² = 17
Read more on quadratic functions here: brainly.com/question/14201243
#SPJ1
The radius of the circle below is 19 mm. Calculate the area of the circle. Give your answer in mm² to 1 d.p. area= 19 mm mm² Not drawn accurately
The universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10).
A = {2, 3, 5, 7}
B = {1, 2, 5, 10}
C = {1, 2, 3, 6}
D = {3, 5, 7)
What is A. n B
What is B n. D^c
What is A^c
What is C. n D
What is B u D ^c
Thank u !!!!!
A ∩ B is the intersection of sets A and B, which is the set of elements that are in both A and B.
A = {2, 3, 5, 7} and B = {1, 2, 5, 10}, so A ∩ B = {2, 5}.
B ∩ D^c is the intersection of set B and the complement of set D, which is the set of elements in B that are not in D.
B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B ∩ D^c = {1, 10}.
A^c is the complement of set A, which is the set of elements in U that are not in A.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 7}, so A^c = {1, 4, 6, 8, 9, 10}.
C ∩ D is the intersection of sets C and D, which is the set of elements that are in both C and D.
C = {1, 2, 3, 6} and D = {3, 5, 7}, so C ∩ D = {3}.
B u D^c is the union of set B and the complement of set D, which is the set of elements that are in B or in the complement of D, or both.
B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B u D^c = {1, 2, 4, 5, 6, 8, 9, 10}.
Thus, this can be the universal set.
For more details regarding universal set, visit:
https://brainly.com/question/24627919
#SPJ1
A single filer had a taxable income of $90,725. Base on table, what is is the tax?
The amount that the taxpayer is owing in taxes is $2,691.05.
We have,
Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.
Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.
The tax payable will equals to:
= 15%*$11,757 + $927.50
= $1,763.55 + $927.50
= $2,691.05
Hence, The amount that the taxpayer is owing in taxes is $2,691.05.
Read more about tax payable
brainly.com/question/897877
#SPJ1
complete question:
Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?
A local wine equipment manufacturer is planning to issue stocks. The company just paid a dividend of $3.60. They now expect to pay dividends to grow at 15% for the next 3 years and thereafter grow at an annual rate of 8%. What should be the price of the stock given these revised forecasts? Assume a rate of return of 16%
a.How does a cumulative voting system allow minority representation in corporations?
Based on these expected future dividends and the rate of return required by investors, the price of the stock should be $414 in year 1, $476 in year 2, $547 in year 3, $93.24 in year 4, $114.53 in year 5, and $138.49 in year 6.
To calculate the price of the stock, we need to first determine the expected future dividends. We know that the current dividend is $3.60, and we can use the dividend growth rate to calculate the expected future dividends.
For the first three years, we can use the 15% dividend growth rate to calculate the expected dividends as follows:
Year 1: $3.60 x 1.15 = $4.14
Year 2: $4.14 x 1.15 = $4.76
Year 3: $4.76 x 1.15 = $5.47
The Gordon growth model is as follows:
P = D / (r - g)
where:
P = price of the stock
D = expected dividend payment
r = rate of return required by investors
g = expected dividend growth rate
Using the formula, we can calculate the price of the stock as follows:
Year 1: P = $4.14 / (0.16 - 0.15) = $414
Year 2: P = $4.76 / (0.16 - 0.15) = $476
Year 3: P = $5.47 / (0.16 - 0.15) = $547
After year 3, the expected dividend growth rate is 8%, so we can use this rate to calculate the price of the stock beyond year 3.
Year 4: P = $5.47 x 1.08 / (0.16 - 0.08) = $93.24
Year 5: P = $5.96 x 1.08² / (0.16 - 0.08) = $114.53
Year 6: P = $6.47 x 1.08³ / (0.16 - 0.08) = $138.49
To know more about dividend here
https://brainly.com/question/29510262
#SPJ1
4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f
The representation of 4.67 on the number line upto 4-decimal places. can be given in image. A picture of numerals along a straight line is called a number line.
A picture of numerals along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
Just to refresh your memory, the entirety of a number is a collection of numbers that contains both zero (0) and all the numbers that count (1, 2, 3,4,5,6), while the number that is natural is a collection of all counting values (1, 2, 3,4, 5, 6). The representation of 4.67 on the number line upto 4-decimal places. can be given in below image.
To know more about number line, here:
https://brainly.com/question/16191404
#SPJ1
Your question is incomplete but most probably your full question was,
Visualise the representation of 4.67 on the number line upto 4-decimal places.
Constantin has a small sunflower farm. One day, he measures and
records the height of each sunflower on his farm. The information is
given below in centimetres:
301, 285, 20, 351, 35, 205, 311, 25, 45, 310, 301, 305
Find the mean height of sunflowers on Constantin’s farm. Round your
answer to two decimal places
The mean height of sunflowers on Constantin's farm is 210.33 centimetres, rounded to two decimal places.
To find the mean height of sunflowers on Constantin's farm, we need to sum up all the heights and divide by the total number of sunflowers.
Adding up all the heights, we get:
301 + 285 + 20 + 351 + 35 + 205 + 311 + 25 + 45 + 310 + 301 + 305 = 2524
There are 12 sunflowers in total, so we divide the sum by 12:
2524 / 12 = 210.33
This means that if we were to select a sunflower at random from Constantin's farm, on average, we would expect it to be about 210.33 centimetres tall.
To learn more about mean height click on,
https://brainly.com/question/15711714
#SPJ1
V(d)V, left parenthesis, d, right parenthesis models Erica's vertical distance from the top of the valley (in kilometers) after walking dd kilometers along the trail.
What does the statement
V
(
2
)
=
T
V(2)=TV, left parenthesis, 2, right parenthesis, equals, T mean?
The correct statement is B. After she had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the function, V(d) models Erica's vertical distance from the top of the valley (in kilometres) after walking d kilometres along the trail.
Therefore, the statement V(2)=T means that after Erica had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.
Learn more about Function here:
https://brainly.com/question/5245372
#SPJ1
The complete question is:
Erica walked down a trail into a valley. V(d) models Erica's vertical distance from the top of the valley (in kilometres) after walking d kilometres along the trail. What does the statement V(2)=T mean?
A-Erica's vertical distance from the top of the valley was the same after she had walked 2km and after she had walked T kilometres.
B- After she had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.
C- After she had walked T kilometres along the trail, Erica's vertical distance from the top of the valley was equal to 2km.
Which addition equation can you make a 10 to add choose 2 that apply
13+15=
49+28=
20+47=
45+35=
We can add 13 and 15, or 49 and 28, or 20 and 47, or 45 and 35 to make 10 in the equations
To add choose 2 numbers to make 10, we can use the fact that 10 is the sum of 6 and 4.
Therefore, we can add a number that is 6 more than 10 and another number that is 4 less than 10.
This gives us the following equations:
13 + 15 = 28, since 13 + 15 = 28 and 10 = 6 + 4
49 + 28 = 77, since 49 + 28 = 77 and 10 = 6 + 4
20 + 47 = 67, since 20 + 47 = 67 and 10 = 6 + 4
45 + 35 = 80, since 45 + 35 = 80 and 10 = 6 + 4
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ1
What is the surface area of this triangular pyramid?
5 yd
5 yd
4.3 yd
7 yd
5 yd
square yards
The surface area of the triangular prism that is shown above is calculated as: 63.25 square yards. .
What is the surface area of a triangular pyramid?The surface area of a triangular pyramid is calculated using the formula below:
SA = A + 3a
where we have:
A = the area of the triangular base of the pyramid
a = the area of one of the pyramid's faces.
Area of one of the pyramid's face (a) = 1/2 * base * height = 1/2 * 5 * 7
a = 17.5 square yards
Area of triangular base (A) = 1/2 * base * height = 1/2 * 5 * 4.3
A = 10.75 square yards
Surface area (SA) = 10.75 + 3(17.5) = 63.25 square yards.
Learn more about surface area of a triangular pyramid on:
https://brainly.com/question/30965326
#SPJ1
For her end of the year party Adriana mixed 6 L of Brand A juice with 9 L of Brand B juice. Brand A contains 52% fruit juice and Brand B contains 12% fruit juice. What percent of the mixture is fruit juice?
A. 28%
B. 20%
c. 30%
A. 28% is the percent of the mixture is fruit juice.
First, we need to find the total amount of fruit juice in the mixture.
For Brand A juice: 6 L x 52% = 3.12 L of fruit juice
For Brand B juice: 9 L x 12% = 1.08 L of fruit juice
Total fruit juice in the mixture: 3.12 L + 1.08 L = 4.2 L
The total amount of the mixture is 6 L + 9 L = 15 L
The percent of the mixture that is fruit juice is:
(4.2 L / 15 L) x 100% = 28%
Therefore, the answer is A. 28%.
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
The maximum grade allowed between two stations in a rapid transit rail system is 2.6% between station and station B, which are 260 feet apart. The tracks rise 5 feet. What is the grade of the track between the stations round answer to the nearest 10th.
The grade of the track between the stations is approximately 1.9%.
How to calculate the grade of the track between the stations round answer to the nearest 10th.The grade of the track is given as a percentage by the change in elevation (climb) divided by the horizontal distance (run) between the two stations:
(climb / run) x 100% = grade
We are given a 5 foot ascent and a 260 foot horizontal distance (run). When we enter these values into the formula, we get:
1.92% = (5/260) x 100% = grade
Rounding to the nearest tenth, the grade of the track between the stations is approximately 1.9%.
Learn more about distance at https://brainly.com/question/17273444
#SPJ1
The diameter of a cylindrical construction pipe is 15 ft . If the pipe is 26 ft long, what is its volume?
Answer:
390
Step-by-step explanation:
what is the surface area of the cylinder
help me teacher does teach us this and it’s on my test
[tex]surface \: area = 2\pi {r}^{2} + 2\pi \: rh \\ 2\pi {(6)}^{2} + 2\pi(6)(15) \\ = 2\pi(36) + 2\pi(90) \\ = 72\pi + 180\pi \\ = 252\pi {in}^{2} [/tex]