It will take 7 men 42 hours to complete the job if they work at the same rate.
If it takes 4 men 6 hours to repair a road, it means that the total work done is 1 job.
The number of man-hours required to complete the job is the product of the number of men and the number of hours
= 4 men x 6 hours
= 24 man-hours
Now, let's find out how many hours it will take for 7 men to do the same job. We can set up a proportion using the man-hours:
4 men / 24 hours = 7 men / x hours
4x = 7 (240)
4x = 168
x = 168 / 4
x = 42
Therefore, it will take 7 men 42 hours to complete the job if they work at the same rate.
Learn more about Proportion here:
https://brainly.com/question/26974513
#SPJ1
Write 5y³ without exponents.
Answer:
can be written as without exponent.Given:To find:Write the given expression without exponent.Solution:Formula to be used:Step 1:Write the expanded form of given expression.Step 2:simplifyorThus, can be written as 125×y×y×y without exponent.Learn more:1) Let us simplify some more questions using the exponent rules. (i) (ii) ... brainly.in/question/196047402) find ( 46656)power of -1/6 brainly.in/question/4383230
Answer: 5y³ can be written without using exponents as 5y multiplied by itself three times:
5y × 5y × 5y
Alternatively, we can also write it as:
5 × y × y × y
which inequality and number line show that a number a, is no more than 10?
The inequality is a < 10
Given that a number a is no more than 10, we need to find the inequality, showing the inequality,
Inequalities are the mathematical expressions in which both sides are not equal.
In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
For example = Olivia is selected in the 12U Softball. How old is Olivia? You don't know the age of Olivia, because it doesn't say "equals". But you do know her age should be less than or equal to 12, so it can be written as Olivia's Age ≤ 12.
This is a practical scenario related to inequalities.
So, the inequality will be =
a < 10
Plotting the inequality,
(check the file attached)
Learn more about inequality click;
brainly.com/question/30231190
#SPJ1
The graph compares temperatures and numbers of cyclists. the equation of the trend line for the scatterplot is y=4x+10
predict the number of cyclists when the temperature is 8 degrees Celsius
A. 38
B. 45
c. 32
D. 42
Answer:
D. 42
Step-by-step explanation:
y=4x+10
substitute x=8
y=4(8)+10
y=32+10=42
Answer:
The answer is 42 cyclists
Step-by-step explanation:
y=4x+10
where,x=Temperature
y=cyclists
y=4x+10;when x=10
Y=4×8+10
y=32+10
y=42
I’m stuck on this question. Can anybody help? Please include the steps
Andrew is working out expenses for his job.
He can claim 45p for each mile that he drives as part of his job.
For one journey he writes down
Mileage at end of journey
Mileage at start of journey
79 165
78 937
(a) Work out how much money Andrew can claim for this journey.
Give your answer in pounds.
£.
Answer: £102.60
Step-by-step explanation:
79165-78937=228
228x45=10260
10260/100=102.60
Otto is sitting on 10 blocks of gold. The blocks are in the shape of right trapezoidal prisms. The trapezoidal base of the prism has bases of 10 inches and 7 inches with a height of 8 inches. The lateral edge of the prism is 19 inches.
a) Upon how many total cubic inches of gold is he sitting? b) Determine the worth of Otto's gold based upon the gold pricing of $13,067.76 per troy pound. Utilize the following information:
• there are 1728 cubic inches in 1 cubic foot.
• there are 1,206.83 pounds of gold in 1 cubic foot.
• there are 0.82 pounds in 1 troy pound.
a number that has more factors than just 1 and itself
factor
2 .
smallest number that all the given denominators divide into evenly
categorical data
3 .
data grouped using non-numerical criteria
equivalent fractions
4 .
fractions with the same numerical value; fractions that are equal to each other
face
5 .
a line segment that goes through the center of the circle to connect two points on the circle
composite number
6 .
a plane figure that is one side of a solid figure
least common denominator
7 .
the measurement of the space inside a plane figure
image
8 .
a shape or object that has been transformed
congruent
9 .
a number that divides evenly into another number
area
10 .
having the same exact size and shape
diameter
match them pls if you are having trouble comment about it.
The matching based on the information given will be:
composite number A composite number is a positive integer that has at least one factor other than 1 and itself. least common denominator The least common denominator (LCD) is the smallest multiple of two or more denominators. categorical data Categorical data is a type of data that can be divided into categories or groups. equivalent fractionsdiameterfaceareaimagefactorcongruentHow to explain the termsA composite number is a positive integer greater than 1 that has at least one factor other than 1 and itself. In other words, it is a number that can be divided by more than just 1 and itself, such as 4.
The least common denominator (LCD) is the smallest number that two or more denominators can be multiplied by to obtain a common denominator.
Categorical data is data that can be sorted into categories or groups based on non-numerical criteria. For example, the colors of cars on a parking lot or the types of pets in a household are both categorical data.
Learn more about composite number on
https://brainly.com/question/192784
#SPJ1
A pair of equations is shown below.
X + Y = 2
Y= 1/2x + 5
If the two equations are graphed, at what point do the lines representing the two equations intersect?
To find the point of intersection between the two lines represented by the given equations, we can solve the system of equations simultaneously.
The given equations are:
1) X + Y = 2
2) Y = (1/2)X + 5
We can solve this system by substituting the value of Y from the second equation into the first equation. Let's proceed with the substitution method:
Substitute Y = (1/2)X + 5 into the first equation:
X + (1/2)X + 5 = 2
Combine like terms:
(3/2)X + 5 = 2
Subtract 5 from both sides:
(3/2)X = -3
Multiply both sides by 2/3 to isolate X:
X = -2
Now, substitute the value of X back into the second equation to find Y:
Y = (1/2)(-2) + 5
Y = -1 + 5
Y = 4
Therefore, the lines represented by the given equations intersect at the point (-2, 4).
15 Points PLEASE HELP ME OUT.
Algebra 1 honors
The quadratic function is defined as follows:
p(x) = 2(x - 3)² - 1.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The vertex is the turning point of the quadratic function, where it changes from decreasing to increasing or vice-versa, hence it's coordinates are given as follows:
(3,-1).
Then:
p(x) = a(x - 3)² - 1.
When x = 0, p(x) = 17, hence the leading coefficient a is obtained as follows:
17 = 9a - 1
9a = 18
a = 2.
Hence the equation is:
p(x) = 2(x - 3)² - 1.
More can be learned about quadratic functions at https://brainly.com/question/31895757
#SPJ1
an equation of the line normal to the graph of y=x^3+3x^2+7x-1
this equation is only valid at the point (a, b) where we found the slope of the normal line. To find the equation of the normal line at a different point, we would need to repeat this process with new values of a and b.
To find the equation of the line normal (perpendicular) to the graph of y = x^3 + 3x^2 + 7x - 1 at a point (a, b), we need to determine the slope of the normal line at that point.
The slope of the tangent line to the curve at (a, b) is given by the derivative:
f'(x) = 3x^2 + 6x + 7
So the slope of the tangent line at x = a is:
m = f'(a) = 3a^2 + 6a + 7
The slope of the normal line is the negative reciprocal of the slope of the tangent line, so:
m_n = -1/m = -1/(3a^2 + 6a + 7)
Now we have the slope of the normal line at (a, b), and we just need to find the equation of the line in point-slope form, using the point (a, b):
y - b = m_n(x - a)
Substituting the expression for m_n, we get:
y - b = (-1)/(3a^2 + 6a + 7)(x - a)
Multiplying both sides by 3a^2 + 6a + 7 to eliminate the fraction, we get:
(3a^2 + 6a + 7)(y - b) = -(x - a)
Expanding and rearranging, we get the equation of the line normal to the graph of y = x^3 + 3x^2 + 7x - 1 at (a, b):
(3a^2 + 6a + 7)y = -x + (3a^2 + 6a + 7)b + a
To know more about slope visit:
brainly.com/question/3605446
#SPJ11
help me this is due tomorrow
One possible transformation is a reflection in the x-axis followed by a dilation centered at the origin with a scale factor of 3.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
Before the dilation, the figure was reflected from the first quadrant to the second quadrant, which is a lateral reflection, hence the figure was reflected over the x-axis.
The height of the blue triangle is of 1 unit, while the height of the larger triangle is of 3 units, hence the scale factor is given as follows:
k = 3/1
k = 3.
More can be learned about dilation at brainly.com/question/3457976
#SPJ1
the salaries of 5 doctors at a private practice are: $145,000, $175,000, $110,000, $190,000, $190,000. what is the median of these salaries? (you do not need to type $ or , in your answer.)
To find the median of salaries of 5 doctors at a private practice, we need to arrange the salaries in order from smallest to largest. The median of these values, since there are 5 values, is the 3rd value which is $175,000.
The subject of your question is Mathematics, specifically the concept of the median in statistics.
The median of a set of numbers is found by arranging the numbers in order from least to greatest, and the median is the middle number in this arrangement.
Hence, in order to find the median of the given salaries, we first arrange them in ascending order: $110,000, $145,000, $175,000, $190,000, $190,000.
Since there are 5 doctors, which is an odd number of observations, the median is the 3rd number ($175,000) considering they are arranged in order from smallest to largest.
For more such questions on Median of Salaries, click on:
https://brainly.com/question/34043269
#SPJ2
two garden plots are to have the same area. One square and one rectangle. The rectangle plot is 4 meters wide and 16 meters long. How large is one side of the square garden plot in meters?
Answer:
8 meters
Step-by-step explanation:
4(16)=64
They have the same area so the area of the square is also 64.
x^2=64
x=8
(Lebl Exercise 2. 2. 12 (a)) Suppose (an)
[infinity]
n=1 is a bounded sequence, and (bn)
[infinity]
n=1 converges
to 0. Prove that (anbn)
[infinity]
n=1 converges to 0
The statement to be proved is that if (an)[infinity]n=1 is a bounded sequence and (bn)[infinity]n=1 converges to 0, then (anbn)[infinity]n=1 converges to 0 as well.
To prove this statement, we can use the squeeze theorem. Let M be a bound for the sequence (an)[infinity]n=1, i.e., |an| <= M for all n. Since (bn)[infinity]n=1 converges to 0, for any ε > 0, there exists an integer N such that |bn| < ε/M for all n ≥ N.
Now, for any n ≥ N, we have
|anbn| = |an||bn| ≤ M|bn| < ε,
where we used the fact that |an| ≤ M. This shows that (anbn)[infinity]n=1 converges to 0 as well, since the absolute value of each term is bounded by ε for n ≥ N.
In other words, we have shown that for any ε > 0, there exists an integer N such that |anbn - 0| < ε for all n ≥ N. This is the definition of convergence to 0, and so we have proven that (anbn)[infinity]n=1 converges to 0.
To learn more about converges click here, brainly.com/question/29258536
#SPJ11
If A= [P q] find additive inverse of A
[r. s ]
Answer:
The additive inverse of A is -A. So, the additive inverse of A = [p q] is -A = [-p -q].
Here's how we can find the additive inverse of a matrix:
Find the additive inverse of each element in the matrix.
Replace each element in the matrix with its additive inverse.
For example, the additive inverse of p is -p. So, the additive inverse of the first element in A is -p.
The additive inverse of q is -q. So, the additive inverse of the second element in A is -q.
Plugging in these values, we get the following:
Additive inverse of A = [-p -q]
Step-by-step explanation:
in an apartment complex with 28 units, 19 of the renters keep a pet. what percentage does not keep a pet? 14.7% 32% 68% 62%
Approximately 32.14% of the renters do not keep a pet.
We know that there are 28 units in the apartment complex. Out of these, 19 renters keep a pet. To calculate the number of renters who do not keep a pet, we subtract the number of renters with pets (19) from the total number of renters (28):
Number of renters without pets = Total number of renters - Number of renters with pets
Number of renters without pets = 28 - 19
Number of renters without pets = 9
Now that we have the number of renters without pets (9), we can calculate the percentage of renters who do not keep a pet. To do this, we divide the number of renters without pets by the total number of renters and multiply by 100:
Percentage of renters without pets = (Number of renters without pets / Total number of renters) × 100
Percentage of renters without pets = (9 / 28) × 100
Percentage of renters without pets ≈ 32.14%
Therefore, approximately 32.14% of the renters in the apartment complex do not keep a pet.
To know more about percentage here
https://brainly.com/question/13729841
#SPJ4
for what value of k will x+k/x have a relative maximum at x=-2
when k = 4, the function x + k/x will have a relative maximum at x = -2.
To find the value of k that will make x+k/x have a relative maximum at x=-2, we can use the first derivative test.
First, we find the derivative of x+k/x with respect to x:
f'(x) = 1 - k/x^2
Next, we set x = -2 and solve for k to make f'(-2) = 0:
f'(-2) = 1 - k/(-2)^2 = 1 - k/4
1 - k/4 = 0
k = 4
what is derivative?
A derivative is a mathematical concept that represents the rate at which a function changes over time or space. It is the slope of a tangent line to a curve at a particular point.
In other words, the derivative of a function f(x) at a point x=a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim[h→0] [f(a+h) - f(a)]/h
The derivative gives us information about how quickly the function is changing at a specific point.
To know more about derivative visit:
brainly.com/question/29144258
#SPJ11
What is the best approximation of the volume, in cubic units, of a sphere of diameter 12?
The best approximation of the volume of a sphere with a diameter of 12 units is approximately 904.78 cubic units.
The formula for the volume of a sphere is V = (4/3)πr^3, where V represents the volume and r represents the radius.
Given the diameter of 12 units, we can find the radius by dividing the diameter by 2: r = 12 / 2 = 6 units.
Now, we can substitute the radius into the volume formula:
V = (4/3)π(6^3)
= (4/3)π(216)
≈ 904.78 cubic units
Using the approximation of π as 3.14, we can calculate the volume as follows:
V ≈ (4/3) * 3.14 * 216
≈ 904.78 cubic units
Therefore, the best approximation of the volume of the sphere with a diameter of 12 units is approximately 904.78 cubic units.
To learn more about volume of a sphere click here
brainly.com/question/21623450
#SPJ11
HELP!! solve each logarithmic equation for the value of the variable. Be sure to check for extraneous solutions
[tex]D:\dfrac{4000}{x} > 0 \wedge x\not =0\\D:x > 0\\\\\\\log\left(\dfrac{4000}{x}\right)=3\\\e^3=\dfrac{4000}{x}\\\\x=\dfrac{4000}{e^3}[/tex]
x^7+3x^5+3x+1
- x^7+5x+10
Answer:
Step-by-step explanation:
Your welcome
. Segment AB is tangent to circle O at B. The diagram is not drawn to scale. If AB = 9 and AO = 12.3, what is the length of the radius (r)? Round your answer to the nearest tenth.
Answer:
8.4
Step-by-step explanation:
C^2-B^2=A^2
12.3^2=151.29
9^2=81
151.29-81=70.29
square root of 70.29
is 8.38
Rounded to the nearest tenth is
8.4 or B
Please help!
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function?
Part B: What does the y-intercept of the graph of the function f(d) represent?
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent?
If you could solve this without logging, that would be great. Thank you
The domain to plot the growth function is 0 ≤ x < 7
The initial radius of the algae is 11 mmThe average rate of change from day 2 to day 7 is 0.114 mm per dayCalculating the domain to plot the growth function?Given that
f(d) = 11(1.01)ᵇ
When the radius is approximately 1179 mm
We have
11(1.01)ᵇ = 11.79
Divide
(1.01)ᵇ = 1.072
Take the logarithm
d = log(1.072)/log(1.01)
Evaluate
d = 6.99
So, the reasonable domain is 0 ≤ x < 7
Interpreting the y-intercept and the average rateHere, we have
f(d) = 11(1.01)ᵇ
The y-intercept is 11
This means tha the initial radius of the algae is 11 mm
For the average rate, we have
f(7) = 11(1.01)⁷ = 11.79
f(2) = 11(1.01)² = 11.22
So, we have
Rate = (11.22 - 11.79)/(2 - 7)
Evaluate
Rate = 0.114
So, the average rate of change from day 2 to day 7 is 0.114 mm per day
Read more about exponential functions at
https://brainly.com/question/2456547
#SPJ1
A bakery is making cupcakes using a cylindrical mold. The cupcake mold has a diameter of 7.5 centimeters and is 5 centimeters tall. Which of the following shows a correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top? Use 3.14 for π.
V = (3.14)(7.5)2(5)
V = (3.14)(3.75)2(5)
V = (3.14)(5)2(7.5)
V = (3.14)(5)2(3.75)
The expression that shows the correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top would be = V = (3.14)(3.75)2(5). That is option B.
How to calculate the volume of the cake needed to fill the mold?To calculate the volume of the cake mold needed, the formula for the volume of a cylinder should be used and it is given below;
Volume of cylinder = πr²h
radius = diameter/2 = 7.5/2 = 3.75
Height = 5cm
π = 3.14
Volume = 3.14×(3.75)²×5
Therefore the correct expression that will determine the volume of cake batter needed to fill the mold would be = Volume = 3.14×(3.75)²×5
Learn more about volume here:
https://brainly.com/question/28795033
#SPJ1
what are the coordinates of the point on the graph?
The coordinates of the point on the graph are (0, -7).
We have,
The concept being used here is the Cartesian coordinate system, which is a system for representing points in a two-dimensional space.
In this system, each point is described by an ordered pair (x, y), where x represents the position along the horizontal x-axis, and y represents the position along the vertical y-axis.
The coordinates are always in an ordered pair.
i.e
(x, y)
Where x is the value of the x-axis and y is the value of the y-axis.
We see that,
The point lies in (0, -7)
Thus,
The coordinates of the point on the graph are (0, -7).
Learn more about coordinates here:
https://brainly.com/question/13118993
#SPJ1
Convert 1111 to binery
Answer:
1111 in binary is 10001010111. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits).
The surface area of a right cone is 364 square inches. If the slant height of the cone is 6.5 inches, what is the radius of the cone in inches? Round to the nearest inch.
The radius of the cone to the nearest inch is equal to 8.0 inches.
How to calculate surface area of a cone?In Mathematics and Geometry, the surface area (SA) of a cone can be calculated by using this mathematical expression:
Surface area (SA) of a cone = πr(l + r)
Where:
l represents the slant height of the cone.r represents the radius of the cone.By substituting the given parameters into the formula for the surface area (SA) of a cone, we have the following;
364 = 3.14 × r(6.5 + r)
115.92 = 6.5r + r²
r² + 6.5r + 115.92 = 0
By solving the quadratic function, we have:
Radius, r = (-20.41 + √4988.4081)/6.28
Radius, r = 7.9966 ≈ 8.0 inches.
Read more on surface area here: brainly.com/question/27812847
#SPJ1
in the cost equation tc = f + vx, x is best described as the:
The cost equation is used to estimate total costs associated with a given level of activity or output, where f is the fixed cost and v is the variable cost per unit of activity. The variable cost component (vx) changes in proportion to the level of activity or output (x), whereas the fixed cost component (f) remains constant regardless of the level of activity.
In the cost equation tc = f + vx, x is best described as the level of activity or the quantity of the input variable. The cost equation is a mathematical representation of the relationship between the total cost of production and the level of activity or the quantity of the input variable. The variable x represents the number of units produced or the amount of resources used in the production process, which can be measured in terms of labor hours, machine hours, or any other relevant unit of measure. The variable v represents the variable cost per unit of activity, and f represents the fixed cost of production.
To learn more about fixed cost : brainly.com/question/30057573
#SPJ11
7) A rectangular picture frame measures 20 cm by 30 cm. A new frame is to be made
by increasing each side length by the same amount. The resulting enclosed area is
to be 1064 cm2. Find the dimensions of the new picture frame.
The dimension of the new picture frame is around 51.49 cm by 61.49 cm in size.
Given that,
The measure of rectangular picture = 20 cm x 30 cm
And the resulting enclosed area = 1064 cm²
Let the length of each side = x
Therefore,
The new rectangular frame will have dimensions = 20 cm + x, 30 cm + x
The new rectangular frame's surface area is:
= (20 + x) x (30 + x).
Since area is given,
So that we can create an equation: 1064 = (20 cm + x) x (30 cm + x)
Increasing the brackets results in: 600 + 50x + x² = 1064
Organizing and making it simpler: x² + 50x - 464 = 0.
By using quadratic formula,
x = (-50 ± 174.96) / 2
Neglecting the undesirable outcome,
x = 62.98 / 2 x = 31.49
Consequently, each side length has increased by around 31.49 cm.
Use this value to determine the new rectangular frame's dimensions:
Length is equal to 20 + 31.49 = 51.49 cm.
Width is equal to 30 + 31.49 = 61.49 cm.
Consequently, the new picture frame is around 51.49 cm by 61.49 cm in size.
Learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ1
The box pot below shows how points the Houston Rockets scored last season. What is the interquartile range (IQR) of their scores?
The value of the interquartile range (IQR) of their scores is,
Interquartile range = 25
Since, WE know that;
A box plot is the 5 -number summary of the set of data.
And, 5 -number summary is name as, the first quartile, median, third quartile, minimum, and maximum.
We have to given that;
The box pot shows the points for the Houston Rockets scored last season.
Now, From given box plot,
First Interquartile = 65
Third Interquartile = 90
Hence, The interquartile range (IQR) of their scores is, difference between Third Interquartile and first Interquartile.
So, We can formulate;
Interquartile range = Third Interquartile - First Interquartile
Substitute the given values, we get;
Interquartile range = 90 - 65
Interquartile range= 25
Therefore, We get;
The interquartile range (IQR) of their scores is,
Interquartile range= 25
Which is difference between Third Interquartile and first Interquartile.
Learn more about interquartile range ( IQR ) visit:
brainly.com/question/4102829
#SPJ1
Match each absolute value inequality in the left side with its solution ser on the right.
The solution is, in the drop down activity, you should listen to each sentence and determine whether the verb is a form of "ser" or "ir" based on the context and conjugation of the verb.
The verb "ser" means "to be" and is used to describe characteristics, professions, and origins. The verb "ir" means "to go" and is used to indicate movement or direction. To determine whether a verb in a sentence is a form of "ser" or "ir", you should look at the context of the sentence and the conjugation of the verb. If the verb is conjugated in a way that indicates it is a form of "ser", then it is likely a form of "ser". If the verb is conjugated in a way that indicates it is a form of "ir", then it is likely a form of "ir".
For example, in the sentence "Ella es bonita" (She is pretty), the verb "es" is a form of "ser" because it is used to describe a characteristic. In the sentence "Voy a la playa" (I'm going to the beach), the verb "voy" is a form of "ir" because it is used to indicate movement or direction.
In conclusion, to answer the questions in the drop down activity, you should listen to each sentence and determine whether the verb is a form of "ser" or "ir" based on the context and conjugation of the verb.
See more about verb in:
brainly.com/question/1718605
#SPJ1
complete question:
1 - escogerdrop down activity 1 attempt left listen to each sentence and indicate whether the verb is a form of ser or ir. questions
