The number of years it would take is approximately equal to 53 years.
How to determine the population after a number of year?In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 + r)^t
Where:
P(t ) represent the population.t represent the time or number of years.I represent the initial number of persons.r represent the exponential growth rate.By substituting given parameters, we have the following:
96627 = 11211(1 + 0.0418)^t
8.61894567835 = (1.0418)^t
By taking the ln of both sides, we have:
Time, t = ln(8.61894567835)/ln(1.0418)
Time, t = 52.60 ≈ 53 years.
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Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
What is the price per cubic inch for the regular size popcorn
the price per cubic inch for the regular size popcorn is #29.85
How to determine the price?You should understand that Price is what a buyer pays to acquire products from a seller. It takes into account the overall value of the offering, including the value of all raw materials and service that went into making an offering, as well as its markup or margin
The popcorn has 6 faces and the area of the popcorn is given as
Area = LBH
Length
Bredth
Height
Area= 3*5*6 = 90 cm²
Therefore, Price is given as $1.99
This implies that 1.99*90 = $179.1
Therefore the price per inch is 179.1/6 = #29.85
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the temperature at 8 a.m. was -8.7 F. At 1 p.m. it was 9.3 F. What integer represents the change in the temperature from morning to afternoon?
The integer that represents the change in temperature from morning to afternoon is 18.
What is integer?The group of counting numbers that can be written without a fractional component includes zero and both positive and negative integers. An integer can, as was already established, be either positive, negative, or zero.
To find the change in temperature from morning to afternoon, we need to subtract the morning temperature from the afternoon temperature:
9.3 F - (-8.7 F) = 9.3 F + 8.7 F = 18 F
Therefore, the integer that represents the change in temperature from morning to afternoon is 18.
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Use the information below to determine the new coordinates of the image under the given translation.
Triangle ABC with vertices
A(0, 7), B(7, 3),
and C(1, 4): (x, y) → (x − 3, y - 4)
The new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).
What is translation?A shape is translated when it is moved up, down, left or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.
To perform the given translation (x, y) → (x − 3, y - 4) on the triangle ABC with vertices A(0, 7), B(7, 3), and C(1, 4), we need to apply the same transformation to each vertex of the triangle and obtain their new coordinates.
For vertex A(0, 7), the transformation gives:
(x, y) → (x − 3, y - 4)
(0, 7) → (0 - 3, 7 - 4)
The new coordinates of A are (-3, 3).
For vertex B(7, 3), the transformation gives:
(x, y) → (x − 3, y - 4)
(7, 3) → (7 - 3, 3 - 4)
The new coordinates of B are (4, -1).
For vertex C(1, 4), the transformation gives:
(x, y) → (x − 3, y - 4)
(1, 4) → (1 - 3, 4 - 4)
The new coordinates of C are (-2, 0).
Therefore, the new triangle A'B'C' after the translation is A'(-3, 3), B'(4, -1), and C'(-2, 0).
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Working with Actual Interest Earned
Debrorah puts $300 in a CD that earns 3.0% APR, compounded
quarterly, for 1 year. She is taxed at a rate of 20% on the interest she
earns. She takes her money out after 9 months and pays the penalty
fee of 1 quarter's interest.
Deposit
PENALTY
7. What is the total amount of interest that Deborah earns, after taxes?
Type answer here.
The account has an annual interest rate of 6.80%, compounded continuously.
What is interst rate?Interest is the cost associated with the boring money or to return on for lending money it is typically expressed as a percent of the principal amount borrowed or lent and usually the paid periodically over the life of loan interest can also be on from investment such as saving account bonds and the other financial instrument.
The interest rate of the account can be calculated as follows:
Rate = ln(1,698.49/1,051)/(8×ln(1))
Rate = 0.0680 or 6.80%
This means that the account has an annual interest rate of 6.80%, compounded continuously.
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The wholesale cost of a dining room table is $1,315,80. The selling price of the table is $1,776.33. What is the markup for the table?
A 10%
B 35%
C 65%
D 90%
well, the markup is 1,776.33 - 1,315,80 = 461.33.
now, if we take 1315.80(origin amount), what is 461.33 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1315.80 & 100\\ 461.33& x \end{array} \implies \cfrac{1315.80}{461.33}~~=~~\cfrac{100}{x} \\\\\\ 1315.8x=46133\implies x=\cfrac{46133}{1315.8}\implies x\approx 35[/tex]
Find each value or measure.
x =
(40 points) will give brainiest for effort
Answer:
x = 5
Step-by-step explanation:
given FH is a diameter , then
arc FH = 180°, that is
FG + GH = 180°
103° + GH = 180° ( subtract 103° from both sides )
GH = 77°
the central angle HIG is equal to the arc that subtends it GH , so
∠ HIG = 77°
∠ EIF and ∠ HIG are vertically opposite angles and are congruent , then
∠ EIF = 77°
the arc EF subtends the central angle EIF , so
EF = 77°
the sum of the 3 arcs = 180° , that is
HD + DE + EF = 180
15 + 18x - 2 + 77 = 180
18x + 90 = 180 ( subtract 90 from both sides )
18x = 90 ( divide both sides by 18 )
x = 5
then arc DE = 18x - 2 = 18(5) - 2 = 90 - 2 = 88°
The expression below is equal to -20g plus a constant term. -8(2.5g-4.25)+5.25 What is the value of the constant term?
Answer:
We can simplify the expression -8(2.5g-4.25)+5.25 by distributing the -8:
-8(2.5g-4.25)+5.25 = -20g + 34 + 5.25
Simplifying further, we can combine the constant terms:
-8(2.5g-4.25)+5.25 = -20g + 39.25
So the value of the constant term is 39.25.
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Sunny Town is symmetric
Mean, because Sunny Town is skewed
Median, because Beach Town is skewed
Mean, because Beach Town is symmetric
Answer:
Whats the question?
Step-by-step explanation:
In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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center (-4, -7), tangent to x = 2
Answer:
(x + 4)^2 + (y + 7)^2 = 36
Step-by-step explanation:
The given information describes a circle with its center at (-4, -7) and tangent to the vertical line x = 2. To determine the radius of the circle, we need to find the distance between the center and the tangent line.
The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by:
d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)
In this case, the equation of the line is x = 2, which can be written as 1x + 0y - 2 = 0. Therefore, A = 1, B = 0, and C = -2. The center of the circle is (-4, -7), so x1 = -4 and y1 = -7. Substituting these values into the formula, we get:
d = |1*(-4) + 0*(-7) - 2| / sqrt(1^2 + 0^2)
d = |-6| / sqrt(1)
d = 6
Therefore, the radius of the circle is 6 units. The equation of a circle with center (h,k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values we have found, we get:
(x + 4)^2 + (y + 7)^2 = 36
This is the equation of the circle that satisfies the given conditions.
Given the figure below .find X and Y to three significant digits.Write your answer in the answer box provided below
Check the picture below.
Make sure your calculator is in Degree mode.
[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]
What are the answers to these questions?
absolute maximum is ? and it occurs at x = ?
absolute minimum is ? and it occurs at x = ?
The absolute maximum value of f(x) is 4.5 and it occurs at x = -0.5, and the absolute minimum value of f(x) is -0.241 and it occurs at x = 0.833
Calculating the absolute maximum and minumum of the functionTo find the absolute maximum and minimum of the function f(x) = 4x^3 - 2x^2 - 5x + 3, we need to take the derivative of the function and set it equal to zero to find the critical points.
f(x) = 4x^3 - 2x^2 - 5x + 3
f'(x) = 12x^2 - 4x - 5
Setting f'(x) = 0, we get:
12x^2 - 4x - 5 = 0
Using the quadratic formula, we get:
x = -0.5 or x = 0.833
Now we need to check the values of f(x) at the critical points and the endpoints of the interval
f(-0.5) = 4(-0.5)^3 - 2(-0.5)^2 - 5(-0.5) + 3 = 4.5
f(0.833) = 4(0.833)^3 - 2(0.833)^2 - 5(0.833) + 3 = -0.241
So the absolute maximum it occurs at x = -0.5, and the absolute minimum occurs at x = 0.833
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Bokamoso rides a bicycle to school every day (taking the same route). If she rides at 16 km/h, it takes her 45 minutes to get to school. 1. How far does Bokamoso ride on the way to school?
5.40 km is the distance Bokamoso ride on the way to school
What is speed, distance and time?
Speed is determined by dividing the distance travelled by the time taken to travel it. It gives the amount of time it took to travel a certain distance divided by the distance travelled.
Speed is inversely correlated with time and directly correlated with distance. As a result, distance equals speed times time, and time equals distance divided by speed; as speed rises, distance travelled will shorten, and vice versa.
Bokamosa rides at 16 km / hr
To get to school = 45 min
= 45 * 0.75 hour
= 0.3375 hr
Distance = Speed * Time
d = 16 * 0.3375
= 5.40 km
Hence, 5.40 km is the distance Bokamoso ride on the way to school.
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10. What is the toxic life of nuclear waste?
O 100,000 years
10,000 years
O 100 years
1 million years
Nuclear waste needs to be safely stored for up to a million years, so the answer is 1 million years.
Is a measure of 30 inches "far away" from a mean of 15 inches? As someone with knowledge of statistics, you answer "it depends" and request the standard deviation of the underlying data.
(a) Suppose the data come from a sample whose standard deviation is 3 inches. How many standard deviations is inches from 15 inches?
(b) Is 30 inches far away from a mean of 15 inches?
(c) Suppose the standard deviation of the underlying data is 10 inches. Is 30 inches far away from a mean of 15 inches?
Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.
what is standard deviation ?The standard deviation of statistics is a measurement of how much a group of data values deviate from their mean (average) value. While a significant standard deviation suggests that the pieces of information are dispersed throughout a broader range of values, a low standard deviation suggests that the data points are generally close to the mean.
given
a) If the sample's standard deviation is 3 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:
z = (30 - 15) / 3 = 5
b) The context of the data and the standard deviation will determine whether 30 inches is distant from a mean of 15 inches.
A departure of 15 inches from the mean, meanwhile, can be viewed as being significantly off the mean if the standard deviation is minimal.
c) If the underlying data's standard deviation is 10 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:
z = (30 - 15) / 10 = 1.5
Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.
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f(x) = x2 + 4; interval [0, 5]; n = 5; use left endpoints
Therefore, the Left Riemann Sum for this function, interval, and number of subintervals is 50.
The left endpoint rule is what?The top-left corner of these rectangles touched the y=f(x) curve. In other words, the value of f at the subinterval's left endpoint determined the height of the rectangle over that subinterval. This technique is called the left-endpoint estimate because of this.
With left endpoints and n = 5 subintervals, we may use the Left Riemann Sum formula to approximate the area under the curve of f(x) = x2 + 4 over the range [0, 5]:
Left Riemann Sum = ∑[i=1 to n] f(x_i-1) Δx
In this case, a = 0, b = 5, n = 5, and we will use the left endpoints, so:
Δx = (5 - 0)/5 = 1
Using the left endpoints, the subintervals and their left endpoints are:
[0,1],[1,2],[2,3],[3,4],[4,5]
[tex]so,\; x_0 = 0, x_1 = 1, x_2 = 2, x_3 = 3, x_4 = 4.[/tex]
Now we can calculate the Left Riemann Sum:
Left Riemann Sum= [tex]f(x_0)\Delta x + f(x_1)\Deltax + f(x_2)\Deltax + f(x_3)\Deltax + f(x_4)\Deltax[/tex]
= f(0)×1+f(1)×1+f(2)×1+f(3)×1 + f(4)×1
= 4+5+8+13+20
= 50
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ixl What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 15 cm 16 cm
We have to calculate the surface area of the cylinder.
It has a base diameter of 16 inches and a height of 15 inches.
The surface area will be equal to the sum of the area of the base, the area of the top (that is equal to the area of the base) and the lateral surface.
The area of the base can be calculated as:
[tex]\text{A}_{\text{b}}=\dfrac{\pi \text{D}^2}{4}[/tex]
[tex]\text{A}_{\text{b}}=\dfrac{3.14\times16^2}{4}[/tex]
[tex]\text{A}_{\text{b}}=\dfrac{3.14\times256}{4}[/tex]
[tex]\text{A}_{\text{b}}=200.96[/tex]
The lateral surface will be equal to the circumference of the base times the height. We then can calculate it as:
[tex]\text{A}_\text{l}}=(\pi \text{D})\text{h}[/tex]
[tex]\text{A}_\text{l}}=3.14\times16\times15[/tex]
[tex]\text{A}_\text{l}}=753.60[/tex]
Then, we can calculate the surface area of the cylinder as:
[tex]\text{A}=\text{A}_\text{b}}+\text{A}_\text{l}}+\text{A}_\text{l}}[/tex]
[tex]\text{A}=200.96+200.96+753.60[/tex]
[tex]\text{A}=1155.52[/tex]
Answer: the surface area is 1155.52 in²
Ian has a deck that measures 20 feet by 10 feet. He wants to increase each dimension by equal lengths so that its area is tripled. By how much should he increase each dimension?
Answer:
10 feet
Step-by-step explanation:
Let's start by finding the current area of the deck:
Area = length x width = 20 ft x 10 ft = 200 sq ft
If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:
Length = 20 ft + x
Width = 10 ft + x
The new area of the deck will be:
New Area = (20 ft + x) x (10 ft + x)
We know that Ian wants the new area to be triple the original area of 200 sq ft, so:
New Area = 3 x 200 sq ft
New Area = 600 sq ft
Substituting this into the equation above and solving for "x", we get:
(20 ft + x) x (10 ft + x) = 600 sq ft
200 + 30x + x^2 = 600
x^2 + 30x - 400 = 0
(x + 40) (x - 10) = 0
We discard the negative solution, and we get:
x = 10 ft
Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.
To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.
If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.
Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.
Ian should increase both the sides by 10 feet each.
This is a simple mathematics problems related to the topic of mensuration.
Firstly we calculate the current area of the deck:
Area of the deck (rectangle) = l x b
Area of the deck (rectangle) = 20 x 10
Area of the deck (rectangle) = 200 square feet
Since Ian wants to triple the area of the deck, the required area is 600 square feet.
We now look at pairs of numbers multiplying which will give us 600:
(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)
Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.
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x^2+y^2+6x+2y-6=0 what is the center of this circle? what is the radius of this circle?
Answer:
center : (-3, -1) radius : 4
The table below shows the numbers of two to five bedroom houses in the Belmont Neighborhood. What is the mean number of bedrooms in a house in this neighborhood?
Number of bedrooms Frequency
2 7
3 35
4 56
5 27
The mean number of bedrooms in a house in this neighborhood will be: 3.824.
How to determine the mean number of bedroomsIn order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.
Next, we will add the products, and then divide by the total frequency. So we can start as follows:
(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478
Total frequency = 7 + 35 + 56 + 27 = 125
Therefore, the mean number of bedrooms = 478 / 125 approximately 3.824
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Find the critical value t
The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.
What is Critical value?In statistics, the critical value is a value that is used to determine whether to reject the null hypothesis in a hypothesis test. It is based on the chosen level of significance, which is the maximum probability of making a Type I error (rejecting a true null hypothesis). The critical value is determined by the sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.
To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.
Using a t-distribution table with 21 degrees of freedom (n-1), we find that the critical value for a 99% confidence level is approximately 2.819.
Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).
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PLEASE HELP SOLVE MATH
The equation of the form y = c + b logₐX is y = -3 + 3 Log₃X
How to derive the equation?Recall that Slope-intercept form of a linear equation is where one side contains just “y”. It looks like y = mx + “b” where “m” and “b” are numbers. This form of the equation is very useful because the coefficient of "x" (the "m" value) is the slope of the line and the constant (the "b" value) is the y-intercept at (0, b)
The equation of the line is give as
y-y₁ = m(x-x₁) + c
Where m is the slope and c is the intercept
This implies that
y -3 = m(x -2)
But slope is given as m = (y₂ - y₁)/(x₂-x₁)
m = (9-3)/ 4-2) = 6/2 = 3
Then, the equation is
y - 3 = 3x - 6
Collecting like terms we have
y = 3x -6+3
y = 3x -3
Writing this in the form y = c + b logₐX
y = -3 + 3 Log₃X
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The equation of the function in the form y = c + b log_a(x) is y = logₓ2
Calculating the equation of the functionWe can start by assuming that the equation is of the form y = c + b log_a(x), where c and b are constants and a is the base of the logarithm.
Using the point (2, 3), we get:
3 = c + b log_a(2)
Using the point (4, 9), we get:
9 = c + b log_a(4)
Simplifying the second equation using the logarithmic identity
loga(4) = 2 loga(2), we get:
3 + 2b loga(2) = 9
Substituting the first equation into this one, we get:
3 = 9 - 2b loga(2)
So, we have
-6 = - 2b loga(2)
Divide
bloga(2) = 3
So, we have
b = 3 / log_a(2)
Substituting this value of b into the first equation, we get:
3 = c + b log_a(2)
3 = c + 3 / log_a(2) * log_a(2)
So, we have
c = 0
Therefore, the equation of the curve is y = (2 / log_a(2)) log_a(x)
We can simplify this equation by using the logarithmic identity log_a(x^b) = b log_a(x):
y = 2 log_a(x) / log_a(2)
y = (2 / log(2)) log(x)
So the final equation is:
y = logₓ2
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There is a 25% chance that a vowel is drawn from a bag of random letter tiles. what is the probability of drawing a vowel, placing it back in the bag, and then drawing a consonant
The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.
The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.
The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:
P(vowel and consonant) = P(vowel) x P(consonant)
= 0.25 x 0.75
= 0.1875
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Matt can save $225 per month that he puts into a savings
account earning 5% annual interest. How much will he have
saved after 2 years?
Answer:
FV ≈ $5,673.56
Step-by-step explanation:
To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))
where:
FV is the future value of the annuity
P is the periodic payment (in this case, $225 per month)
r is the interest rate per year (in this case, 5%)
n is the number of years (in this case, 2)
Substituting the given values, we get:
FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))
Using a calculator, we get:
FV ≈ $5,673.56
Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.
If you horizontally…
Check the picture below.
so following the template below, a shift 2 units to the left, means C=2
[tex]G(x)=\sqrt{x+2}[/tex]
What number increased by 3.5% of itself equals 621?
Answer:
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.
Answer: 138
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.
Chef Lori uses 1 1/4 cup of milk for every 3/4 cup of broth in her soup recipe. This recipe will feed 4 people. Lori is making soup for a banquet that will feed 120 people. How many gallons of milk and broth combined does she need.
Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:
(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth
To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:
(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth
To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):
50/16 = 3.125 gallons of milk
30/16 = 1.875 gallons of broth
Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.
Step-by-step explanation:
Which expression represents the phrase The sum of w and twenty
A. 20w
B. w + 20
C. w^20
D. 20 x w
A student attempted to solve the system 5x + 2y = 10 and 10x + 2y = 1 by graphing. The graph and the conclusion are
below. What can you say about the student's work?
y
-10x + 2y = 1
5x + 2y = 10
The soluion is ().
O The solution is incorrect because the student did not correctly identify the intersection.
O The solution is correct and the lines are graphed correctly.
O The solution is correct, but the lines were graphed incorrectly.
O The solution is incorrect because the lines are not graphed correctly.
Answer:
Option A: The solution is incorrect because the student did not correctly identify the intersection.
Step-by-step explanation:
Solve by elimination method.
5x + 2y = 10; -10x + 2y = 1
Multiply the second equation by -1, then add the equations together.
(5x + 2y = 10)
-1 (-10x + 2y = 1)
Forms:
5x + 2y = 10
10x - 2y = -1
Add these equations to eliminate y.
15x = 9
Then solve 15x = 9 for x:
15x = 9
15/15 = 9/15 (Divide both sides by 15)
x = 3/5
Now that we've found x let's plug it back in to solve for y.
Write down the original equation:
5x + 2y = 10
Substitute 3/5 for x in:
5x + 2y = 10:
5(3/4)+2y=10
2y+3=10
2y+3-3=10+-3
2y=7
2y/2 = 7/2
y = 7/2
x = 3/5 and y = 7/2.
Comparing the identified answers to the one found by the students, it can be concluded that Option A: The solution is incorrect because the student did not correctly identify the intersection.