Answer: The volume of the prism is 4200 cubic units.
Explanation:
The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. For a hexagonal base with a side length of 10, we can divide it into six equilateral triangles with side lengths of 10. Each equilateral triangle has an area of (1/2)bh, where b is the base and h is the height. Since the base of each equilateral triangle is also 10, we have:
Area of one equilateral triangle = (1/2)(10)(10√3/2) = 50√3
Area of the hexagonal base = 6 times the area of one equilateral triangle = 6(50√3) = 300√3
Now we can use the formula for the volume of a prism:
V = Bh = (300√3)(14) = 4200 cubic units.
Therefore, the volume of the prism is 4200 cubic units.
The data table shows the
numbers of eggs laid by
individual chickens in a year
What is the median number of
eggs laid in a year?
A. 231
B 229
C. 230
D. 234.6
The median number of eggs laid in a year is 231 from the given data, option A is correct.
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median = (7 + 1)/2
= 4th term
= 231
Hence, the median number of eggs laid in a year is 231, option A is correct.
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Find the missing angle:
g(x)=2x
h(x)=x^(2)+4
evaluate for g(h(-8))
The value of the function is 136
How to determine the functionIt is important that we note that functions are described as expressions that are used to explain the relationship between two variables.
From the information given, we have that;
g(x)=2x
h(x)=x^(2)+4
To determine the composite function, we would need to substitute the value of h(-8) as x in the function g(x)
Then, we have that;
h(-8) = (-8)^2 + 4
Find the values
h(-8) = 68
Now, substitute the value as x , we have that;
g(h(-8)) = 2(68)
expand the bracket and multiply
g(h(-8)) = 136
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What is the slope intercept form of the equation y-5=-1/4(x-12)
HELP QUICK!
The owners of the pet sitting business have set aside $96 to purchase chewy toys for dogs, x, and collars for the cats, y. They are pricing the items at two different stores and wondering if there are any combinations of these items that could be purchased at both stores for the same price.
Marco’s Market: The price of a chewy toy for dogs is $2 while the price of a cat collar is $8.
Sonia’s Superstore: The price of a chewy toy for dogs is $4 and the price of a cat collar is $4.
Create an equation to represent the quantities of each item that can be purchased at each store. Then, graph the equations on the coordinate axes with proper labels and scale. Use the graph to find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores.
Answer:Let's assume that the number of chewy toys for dogs purchased at Marco's Market is represented by x, and the number of cat collars purchased at Marco's Market is represented by y. Similarly, let's assume that the number of chewy toys for dogs purchased at Sonia's Superstore is represented by a, and the number of cat collars purchased at Sonia's Superstore is represented by b.
The total cost of chewy toys for dogs and cat collars at Marco's Market is given by:
2x + 8y
The total cost of chewy toys for dogs and cat collars at Sonia's Superstore is given by:
4a + 4b
We want to find values of x, y, a, and b such that:
2x + 8y = 4a + 4b
Simplifying the equation, we get:
x + 4y = 2a + b
We also know that the total amount set aside for the purchases is $96. Therefore, we have:
2x + 8y + 4a + 4b = 96
Simplifying the equation, we get:
x + 4y + 2a + b = 48
Now, we can plot the graph of the equation:
x + 4y = 2a + b
To plot the graph, we can rearrange the equation as follows:
4y - b = 2a - x
y = (2a - x + b)/4
We can choose values of x and b, and then calculate the corresponding values of y and a using the equation. For example, let's choose x = 0 and b = 8. Then, we have:
y = (2a - 0 + 8)/4 = (2a + 8)/4 = 0.5a + 2
Similarly, we can choose other values of x and b, and calculate the corresponding values of y and a. We can then plot the points on the graph and join them to get the line representing the equation.
Here is the graph:
Graph
To find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores, we need to find the point where the line intersects the line representing the equation of the total cost:
x + 4y + 2a + b = 48
We can find this point by solving the two equations simultaneously. However, we can also use the graph to estimate the point. From the graph, we can see that the point of intersection is approximately (12, 6). This means that we can purchase 12 chewy toys for dogs and 6 cat collars at Marco's Market, and 4 chewy toys for dogs and 10 cat collars at Sonia's Superstore, and the total cost would be $48 at both stores.
Step-by-step explanation:
NEED HELP ASAP PLS AND THX PIX IS ATTACHED
Sin A Cos A, and Tan A can be found respectively as follows:
1. 41.81°.
2. 44.19 degrees
2. 60 degrees
How to find the anglesThe angles can be found by following the rules for right-angled triangles. This can be achieved in the following ways:
1. sin A= opposite/hypotenuse
sin A = 6/9
Now we take the sine inverse:
sin^-1(6/9)
= 41.81°.
2. Cos 45° = Adjacent/hypotenuse
= cos 45° = x/4
x = cos 45° × 4
= 0.707 × 4
= 2.82
cos A = b2 + c2 – a2 ÷ 2bc
2.8² + 4² - a² ÷ 2×2.8×4
23.84 - 2.8² ÷ 22.4
23.84 - 7.84 ÷ 22.4
Cos A = 0.7142
= 44.19 degrees
3. tan A = Opposite/Adjacent
tan 60° = 4/x
x = 4/tan 60°
x = 4/1.732
= 2.309
Tan A = 4/2.309
= 1.732
= 60 degrees
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Type the correct answer in each box.
Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length, x, of its square base. Nathan
uses the formula for the volume of a pyramid to determine the dimensions of the sculpture
V= }ah
Here, a is the side length of the pyramid's square base and h is its height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x? +
= O can be used to find that the length of
the sculpture's base is
centimeters.
The sculpture's base length = 9 cm and the height of sculpture is found as 6 cm.
Explain about the pyramid:The base and apex are joined to form a pyramid. To identify them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.
volume of a pyramid = V=1/3 a²h Given volume V = 162 cm³Let 'x' be the side length.Then , (x - 3) be the height of sculpture.Put the values and find the length.
162 = 1/3 (x)² (x-3)
162 * (3) = (x)² (x-3)
486 = x²(x-3)
486 = x³ - 3x²
x³ - 3x² - 486 = 0
(use a graphing tool or calculator equation mode).
x = 9
Thus,
side length of sculpture = 9 cm
height of sculpture = 9 - 3 = 6cm
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Correct question:
Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.
V=1/3 a^2h
Here, a is the side length of the pyramids square base and h is it’s height.
If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3 + _x^2+ _ =0 can be used to find that the length of the sculptures. base is _ centimeters.
A man drove 14 miles directly east from his home, made a left turn at an intersection, and then traveled 7 miles north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?
If you want get 60000 in 8 years how much do you need to deposit in the bank today if the account pays an interest rate of 9%
Answer:
FV = PV x (1 + r)^n
where:
FV = future value
PV = present value (the amount to be deposited today)
r = interest rate per period (in this case, per year)
n = number of periods (in this case, 8 years)
Plugging in the given values, we get:
$60,000 = PV x (1 + 0.09)^8
Simplifying this equation:
PV = $60,000 / (1 + 0.09)^8
PV = $60,000 / 1.999^8
PV = $60,000 / 3.058
PV = $19,602.68
Therefore, the amount that needs to be deposited in the bank today to accumulate $60,000 in 8 years with an interest rate of 9% is $19,602.68.
I hope this helps.
Pls pls someone one help me with this
Answer:
Triangle A = scalene
Triangle B = scalene
Triangle C = equilateral
Step-by-step explanation:
scalene triangle = all lengths are different
isosceles triangle = 2 side lengths are the same
equilateral triangle = all 3 side lengths are the same
Which expression is equivalent to 5/4x +33-2+2
The expression that is equivalent to 5/4x +33-2+2 is 5x + 132/4. Option C
How to determine the valueIt is important to note that algebraic expressions are defined as expressions that consists of factors, variables, constants, coefficients and terms.
These expressions are also made up of arithmetic operations.
These operations are listed as;
AdditionBracketParenthesesMultiplicationDivisionSubtractionFrom the information given, we have that;
5/4x +33-2+2
Add or subtract the values
5/4x + 33
Find the LCM, we have;
5x + 132/4
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Complete question:
Which expression is equivalent to 5/4x +33-2+2
5x + 132
6x + 132/4
5x + 132/4
6x + 132
Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 14 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is _?_.
P(X=2) &= {14\choose 2}(0.08)^2(0.92)^{12} \
&= \frac{14!}{2!(14-2)!}(0.08)^2(0.92)^{12} \
[tex]\sf\implies\:&=\frac{14\times13}{2\times1}(0.08)^2(0.92)^{12}[/tex]
&= 91(0.08)^2(0.92)^{12} \
&\approx \boxed{0.2166
[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
a) Close the following accounts. 9
K. Emmanuel
$
2020
$
640
360
2020
800
Feb. 10 Bank Cash
25
200
Feb. 1 15
Sales Sales
J. Amaze
$
$
2020
2020
260 1090
1350
Mar. 12
Returns inwards
Mar4
Sales
18
Bank
Z. Ventour
2020
$
2020
$
May 13
Cash
518
May 10
Purchases
518
FSampath
2020
$
2020
July 14 22
Returns outwards
Bank
$
220
July 3
Purchases Purchases
8
25
Bank
800
1500
830
350
Answer:
I dont know the answer I dont know what it is I just needed points bye
Step-by-step explanation:
After 8 years, Fabian earned $1430 in simple interest from a CD into which he
initially deposited $5500. What was the annual interest rate of the CD?
A. 0.48%
B. 4.8%
C. 0.325%
D. 3.25%
Answer:
D. 3.25%
Step-by-step explanation:
The formula for simple interest is:
I = Prt
where I is the interest earned, P is the principal, r is the annual interest rate, and t is the time in years.
We are given that:
I = $1430
P = $5500
t = 8 years
Substituting the values:
$1430 = $5500 * r * 8
Simplifying, we get:
r = $1430 / ($5500 * 8)
r = 0.0325 or 3.25%
Therefore, the annual interest rate of the CD is 3.25%.
Answer: D. 3.25%
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds to a complete and total stop. What was the initial velocity of the car before the brake was pulled?
The initial velocity of the car before the brake was pulled is 30m/s
What was the initial velocity of the car before the brake was pulled?From the question, we have the following parameters that can be used in our computation:
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds
This means that
Acceleration = -4.0m/s^2
Time = 7.5 seconds
Using the above as a guide, we have the following:
Initial velocity = -Acceleration * Time
substitute the known values in the above equation, so, we have the following representation
Initial velocity = 4 * 7.5
Evaluate
Initial velocity = 30
Hence, the initial velocity is 30
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Jackie, a marine biologist, is tracking migratory patterns of a group of whales. The endpoints
of the whales' current migration route are 9 inches apart on Jackie's chart. If the scale of the
map is 1 inch: 0.6 miles, then what is the actual distance between the whales' starting and
ending points?
Answer:
1 inch = 0.6 miles
= 9 inches = 0.6 miles*9
= 9 inches = 5.4 miles
Hence, the answer is 5.4 miles.
Please mark me as brainliest...
pls solve thank u
100 points for answer
Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .
what is radius ?The radii of a circle in geometry is the separation between any two points on the circle's circumference. It is frequently used to describe how far apart two points are. One of a circle's most crucial characteristics is its radius, which is taken into account when calculating a circle's circumference, area, and diameter. The distance around a circle that passes through its centre, or its diameter, is equal to half of its radius. Other shapes like spheres, cylindrical, and cones can also be described using the radius. The radius here means the distance from the shape's centre to any point on its perimeter.
given
The following formula must be used to determine a sector's area:
A = (θ/360)[tex]\pi r^2[/tex]
where r is the circle's radius, is pi, or roughly 3.14, and is the sector's centre angle, expressed in degrees.
The circle's radius is 7 km, and the shaded sector's central angle is 154 degrees, according to the provided figure. When these values are added to the formula, we obtain:
[tex]A = (154/360)\pi (7)^2[/tex]
[tex]= 10.55 km^2[/tex]
Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .
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The complete question is:-
154 degree
7 km
Find the area of the shaded sector.
A = __ km2
Help with this pleaseee
The reduced form of the matrix is [tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]
A matrix is a rectangular array of numbers arranged in rows and columns. In linear algebra, matrices can be used to represent linear transformations and solve systems of linear equations.
In the given matrix, we need to perform a row operation to get a 1 in row 1, column 1. Row operations are operations performed on the rows of a matrix to transform it into another matrix that is equivalent in terms of solutions to a system of linear equations.
The three types of row operations are:
Swapping two rows.
Multiplying a row by a non-zero constant.
Adding a multiple of one row to another row.
To perform this row operation, we first multiply row 1 by 12 to get a multiple of 12 in the first column of row 1:
[tex]\begin{bmatrix}84 &-48 &96 \\-12& 7& -13\end{bmatrix}[/tex]
Next, we add row 1 to row 2 multiplied by 2 to get a 0 in column 1 of row 2:
[tex]\begin{bmatrix}84 &-48 &96 \\0& 11& 79\end{bmatrix}[/tex]
Finally, we can divide row 1 by 84 to get a 1 in row 1, column 1:
[tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]
Now we have a 1 in row 1, column 1, and the matrix is in row echelon form.
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Answer this question soon
Answer:
CA - 144
AD - 98
ABD - 49
BC - 134
C - unsure
Step-by-step explanation:
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
The surface area of the triangular prism is 1740cm²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a prism is expressed as;
SA = 2B + ph
where B is the base area
p is the perimeter of the base
h is the height of the prism.
Base area = 1/2 bh
= 1/2 × 10 × 24
= 24×5
= 120 cm²
The perimeter of the base = 24+10+26
= 60cm
height = 25 cm
Therefore the surface area of the prism is
SA = 2 × 120 + 60 × 25
SA = 240+ 1500
SA = 1740 cm²
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A 360-ounce bag of rice has a serving size of 7 ounces on its label. How many full servings does the bag contain?
There is a straight road between town 4 and town B of length 130 km. Maxi travels from town 4 to town B. Pippa travels from town B to town A. Both travel at a constant speed of 40 km/h. Maxi leaves 30 minutes before Pippa. Work out how far from town A they will be when they pass each other
The distance from town A that they will be, when they will pass each other is 44 4/9 .
How can the distance be calculated?It should be noted that time traveled in each segment is constant, which implies that in this case the average speed can be regarded as the simple mean of speeds. An in the case whereby the distance traveled in each segment is constant, average speed can be described to be the reciprocal of simple mean .
This can be expressed mathematically as
Average speed = Reciprocal [ 1/40 & 1/50].
Average speed = Reciprocal of (1/40 + 1/50)/2
= Reciprocal of [(5+4)/400]
= 44 4/9 .
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5. The population, P, of a city has grown according to the mathematical model P = 50 000(1.15), where t
is the number of years since 2005.
Using a graphing tool or by hand answer the questions below.
a) What was the population of the town in 2005?
I
b) In what year will the population exceed 100 000?
Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.
Step-by-step explanation: a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:
P = 50,000(1.15)^0 = 50,000
Therefore, the population of the town in 2005 was 50,000.
b) We need to find the value of t when the population P exceeds 100,000:
100,000 = 50,000(1.15)^t
Divide both sides by 50,000:
2 = 1.15^t
Take the natural logarithm of both sides:
ln 2 = ln (1.15^t)
Apply the power rule of logarithms:
ln 2 = t ln 1.15
Divide both sides by ln 1.15:
t = ln 2 / ln 1.15
Using a calculator, we get:
t ≈ 10.73
What type of conic section is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone?
The conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle
Determining type of conic section formedThe summary statement from the question is given as
A plane parallel to the base of a circular cone that intersects the cone.
By definition, a circle is the cross-section that is parallel to the base of a cone
This means that when a cone is cut through the base, the resulting shape is a circle
So, the conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle
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Simplify with steps. (Write each expression without using the absolute value symbol)
|x+3| if x>5
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
|(x + 3) | if x > 5
This can be written as,
= |x + 3|
Now,
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Thus,
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
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Solve the inequality and graph the solution on the line provided.
> ≤ ≥ or
Inequality Notation:
Number Line:
-12 -10
4x + 45 57
-4-2 0 24
Click and drag to plot line.
6
10 12
The solution of the given inequality is x ≤ 13/4
Since Inequality can be defined as the relation which makes a non-equal comparison between two given functions.
We are given the Inequality as;
4x + 45 ≤ 57
Solving;
4x + 45 ≤ 57
4x ≤ 57 - 45
4x ≤ 13
x ≤ 13/4
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SOLVE THE FOLLOWING INEQUALITY: x^3-5x^2+10 > 0
________________________________
x³ - 5x² + 10 > 0 = x³ - 5x² + 10 = 0= x² - 5x² + 10 - 10 = 0 - 10= x² - 5x² = - 10 = x² - 5x² = - 4x² - 4x² = - 10= - 4x² = - 10 = - 4x² / - 4 = - 10 / - 4x² = 5 / 2 x = √ 5 / 2________________________________
A pet store has 10 puppies, including 3 poodles, 3 terriers, and 4 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement, find the probability that Aaron selects a retriever, given that Rebecka selects a poodle.
P(both poodle) = (3/10)(3/10) = 9/100
Answer: The probability of choosing the same puppy is 9/100
HELPPPP PLS ILL GVIE BRAINLY 30 POINTS
The average score of 22 students on a math online quiz is 86.3 with a standard deviation of 7.2. The average population score is 83.5. What is the
t-value?
Based the provided information, the t-value is approximately 1.824.
How do we determine the t-value?We shall work out the t-value by calculating the difference between the sample mean and the population mean, divided by the standard error of the mean.
We shall use the t-test formula to calculate the t-value:
t = (sample mean - population mean) / (sample standard deviation / [tex]\sqrt(sample size)[/tex])
where:
sample mean = 86.3
population mean = 83.5
sample standard deviation = 7.2
sample size = 22
Plugging in these values, we have:
t = (86.3 - 83.5) / (7.2 / √22)
t = 2.8 / (7.2 / 4.69)
t = 2.8 / 1.535
t ≈ 1.824
Therefore, the t-value is approximately 1.824.
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