The volume of the right prism if bases are 15 cm apart is 405√3/2 cm^3.
The volume of a right prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a regular hexagon with one side measuring 6 cm and the height of the prism is 15 cm.
To find the area of the base, we can use the formula for the area of a regular hexagon: [tex]A = (3√3/2)s^2[/tex], where s is the length of one side.
Plugging in the value of s = 6 cm, we get:
[tex]A = (3√3/2)(6 cm)^2 = 54√3/2 cm^2[/tex]
Now we can plug this value into the formula for the volume of the prism:
V = Bh = ([tex]54√3/2 cm^2)(15 cm) = 405√3/2 cm^3[/tex]
So the volume of the prism is 405√3/2 cm^3.
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A company makes wax candles in the shape of a rectangular prism. Each candle is 5 inches long, 4 inches wide, and 7 inches tall. How much wax will they need to make 420 candles?
The company will need 58,800 cubic inches of wax to make 420 candles.
How much wax will they need to make 420 candles?To calculate the amount of wax required to make 420 candles,
We need to first calculate the volume of wax required to make one candle,Then multiply that by the total number of candles to find the total amount of wax required.The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.
So, we have
V = 5 in x 4 in x 7 in = 140 cubic inches
To find the total amount of wax required to make 420 candles,
We have
Total amount of wax = 140 cubic inches/candle x 420 candles
= 58,800 cubic inches
Hence, the company needs 58,800 cubic inches
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x + sin x, if x < 0
F(x) = { 2, if x=0
2/(1+x^2), if x > 0
a) Determine if f is continous from the left at x =0
b) Determine if f is continous from the right at x =0
c) Determine if f is continous at f = 0
"f " is continuous at x = 0.
a) To determine if f is continuous from the left at x = 0, we need to evaluate the limit of f(x) as x approaches 0 from the left. This means we need to use the first piece of the function, x + sin x, since this is the piece that applies when x < 0:
lim(x->0-) f(x) = lim(x->0-) (x + sin x) = 0 + sin 0 = 0
Since the limit exists and is equal to the value of the function at x = 0 (which is 2), f is continuous from the left at x = 0.
b) To determine if f is continuous from the right at x = 0, we need to evaluate the limit of f(x) as x approaches 0 from the right. This means we need to use the third piece of the function, 2/(1+x^2), since this is the piece that applies when x > 0:
lim(x->0+) f(x) = lim(x->0+) (2/(1+x^2)) = 2/(1+0^2) = 2
Since the limit exists and is equal to the value of the function at x = 0 (which is 2), f is continuous from the right at x = 0.
c) To determine if f is continuous at x = 0, we need to make sure that the limits from the left and right both exist and are equal to each other and to the value of the function at x = 0. We already found that the limits from the left and right are both equal to 2, which is also the value of the function at x = 0. Therefore, f is continuous at x = 0.
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A person eats 3 slices of pie that has a radius of 4 inches and
an arc length of 45°.
What is the area of the amount of pie the person has eaten?
The area of the amount of pie the person has eaten is equal to the area of a sector with 45° central angle. The area is 6.28 square inches.
The area of the amount of pie the person has eaten can be found using the formula for the area of a sector, which is
A = (θ/360)πr²
where θ is the central angle of the sector (in degrees), r is the radius of the circle, and π is the constant pi.
In this case, θ = 45° (the arc length),
r = 4 inches (the radius of the pie), and
π = 3.14 (the constant pi).
Plugging these values into the formula, we get:
A = (45/360)π(4)²
Simplifying the equation, we get:
A = (0.125)π(16)
A = 2π
A = 6.28 square inches
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Find the slope of the line through the points (-2, -8) and (8, -8)
Answer:
The two points given are (-2, -8) and (8, -8), which lie on a horizontal line. Since the line is horizontal, the slope is zero.
To see this, we can use the formula for the slope of a line between two points:
slope = (y2 - y1)/(x2 - x1)
Substituting the coordinates of the two given points, we get:
slope = (-8 - (-8))/(8 - (-2)) = 0
Therefore, the slope of the line through the points (-2, -8) and (8, -8) is 0.
Step-by-step explanation:
Answer: d = √(Δy2 + Δx2) = √(02 + 102) = √100 = 10
Step-by-step explanation:
if point a is at (6,2 on coordinate plane and point B is located at (-4,2) what is the distance between the two points
explain please
Answer: 10
Step-by-step explanation:
Since both points have the same y value, we just need to find the change of x, which would be the distance of the points.
Reading the points from left to right on an imaginary graph, point B would come first as it has the lesser x value.
To find the change of x subtract the x value of the second point from the first, so...
6 - (-4) = 10
The change of x = 10
The distance between the points is 10
Hope this helps!
Jason earns $232.50 per week as the manager at Big Bucks Department Store. He is single and claimed
1 allowance last year. How much more will be deducted from his weekly check if he claims no
allowances?
If Jason claims no allowances this year, $17 more will be deducted from his weekly check for taxes compared to last year when he claimed one allowance.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
The amount of money deducted from Jason's paycheck for taxes depends on the number of allowances he claims.
Claiming more allowances reduces the amount of taxes withheld from his paycheck while claiming fewer allowances increases it.
If Jason claimed 1 allowance last year, his employer would have withheld taxes from his paycheck based on that information.
If he claims no allowances this year, more taxes will be withheld.
To calculate how much more will be deducted from his weekly check if he claims no allowances, we need to know his tax bracket and the amount of taxes that will be withheld for each allowance.
Assuming Jason is paid on a weekly basis, we can use the IRS tax withholding tables for 2021 to estimate the additional amount of taxes that will be withheld if he claims no allowances.
Using these tables, we find that for a single person earning $232.50 per week, claiming no allowances would result in an additional withholding of $17 per week.
Therefore, claiming no allowances would result in an additional withholding of $17 per week.
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Help
Answer number 9 algebra 2
Show work
The time can be obtained from 1/0.042 * ln (p(t)/1000)
What is an exponential function?
An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is a variable. The base a is usually a number greater than 1, although it can be any positive number.
Exponential functions have a distinctive characteristic that sets them apart from other types of functions: the value of the function increases or decreases exponentially as the value of x increases or decreases. In other words, the rate of change of the function is proportional to its current value, which results in a rapid growth or decay.
We have that;
p(t) = 1000e^0.042t
p(t)/1000 = e^0.042t
ln (p(t)/1000) = 0.042t
t = 1/0.042 * ln (p(t)/1000)
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The rational expression (20n^(2)-180)/(4n^(2)+36n+72) is not defined for any values of n for which the denominator equals zero. Find the values of n for which the denominator equals zero.
The final values of n for which the denominator equals zero are n = -3 and n = -6.
The rational expression [tex](20n^2-180)/(4n^2+36n+72)[/tex]is not defined for any values of n for which the denominator equals zero. To find the values of n for which the denominator equals zero, we need to solve the equation [tex]4n^2+36n+72 = 0.[/tex]
First, we can simplify the equation by dividing all terms by 4:
[tex]n^2+9n+18 = 0[/tex]
Next, we can use the quadratic formula to find the values of n:
n = [tex](-9 ± √(9^2-4(1)(18)))/(2(1))[/tex]
n = (-9 ± √(81-72))/2
n = (-9 ± √9)/2
n = (-9 ± 3)/2
The two values of n are:
n = (-9 + 3)/2 = -6/2 = -3
n = (-9 - 3)/2 = -12/2 = -6
So the values of n for which the denominator equals zero are n = -3 and n = -6.
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What is the image of (0, 4) after a dilation by a scale factor of 3 centered at the
origin?
Answer:
(0,12)
Step-by-step explanation:
You would multiply 4 x 3 and go up to (0,12) on the y axis.
Helping in the name of Jesus.
Phil spent $21 of his $115 pocket money on eating out for one meal. What percent of Phil's pocket money did he spend on eating out for one meal? Round your answer to the nearest hundredth.
Phil spent 18.26% of his pocket money on eating out for one meal.
How do you calculate the percentage difference between two values?The following is the formula for calculating the percentage difference between two values:
100% of ((new value - old value) old value)
In order to describe the change as a percentage, this formula calculates the difference between the new and old values, divides that difference by the old value, and multiplies the result by 100.
Given that, Phil spent $21 of his $115 pocket money.
Thus,
$21 ÷ $115 × 100% = 18.26%
Hence, Phil spent 18.26% of his pocket money on eating out for one meal.
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A
42
48
B
5x - 35
[?]
C
D
Answer:
x = 25
Step-by-step explanation:
We know
5x - 35 is a right angle, meaning it must be 90 degree.
Let's solve
5x - 35 = 90
5x = 125
x = 25
Two equations are shown.
X^2 = 30 X^3 = 30
The solution of equation x² = 30 will be √30 and -√30. And the solution of equation x³ = 30 is ∛30.
What is the solution to the equation?In other words, the collection of all achievable values for the parameters that fulfill the specified mathematical equation is the suitable repository of the bunch of equations.
The equations are given below.
x² = 30 and x³ = 30
From equation x² = 30, then we have
x² = 30
x = ±√30
x = +√30, -√30
From equation x³ = 30, then we have
x³ = 30
x = ∛30
The solution of equation x² = 30 will be √30 and -√30. And the solution of equation x³ = 30 is ∛30.
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Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -1, 1-i f(x) = 0 = Х 3 ?.
The polynomial f(x) of degree 3 with real coefficients and the given zeros is f(x) = x³ - x² + 4x + 2.
To find a polynomial f(x) of degree 3 with real coefficients and the given zeros, we need to use the fact that if a polynomial has a complex root, then its conjugate is also a root. This means that if 1-i is a root, then 1+i is also a root.
So, our polynomial f(x) has the following roots: -1, 1-i, 1+i.
We can write the polynomial as the product of its factors:
f(x) = (x - (-1))(x - (1-i))(x - (1+i))
Simplifying the factors:
f(x) = (x + 1)(x - 1 + i)(x - 1 - i)
Multiplying the factors:
f(x) = (x + 1)(x² - 2x + 2)
Expanding the polynomial:
f(x) = x³ - 2x² + 2x + x² - 2x + 2
Simplifying the polynomial:
f(x) = x³ - x² + 4x + 2
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38 dollars less than charlie earned.in variables
Answer:
x = c - 38
Step-by-step explanation:
Write a formula for the given measure. Tell what each variable represents. Identify which variable depends on which in the formula.
1. The perimeter of a rectangle with the length of 4 meters.
2. The area of a triangle with a base length of 10 feet.
H i there what is the answer for this
Answer:
t = 56 degree
Step-by-step explanation:
A triangle is 180 degrees.
The angle on the right is a vertical angle to the 34-degree angle, meaning their angles are equal.
We know two angles; one is 90 degrees, and the other is 34 degrees. To find the angle t, we take
180 - 90 - 34 = 56 degree
So, t = 56 degree
Vinne Two weeks ago, the cost to fly from to was 210$. Now the cost is 300$. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Step-by-step explanation:
for % questions always find 100% and/or 1%.
everything else can be easily calculated out of these 2.
the original price of $210 = 100%, as we want to know how many % the new price is different from that.
100% = $210
1% = 100%/100 = 210/100 = $2.10
the new price is $300.
the difference is 300 - 210 = $90
how many % are $90 compared to the original price ?
well, as many as the times 2.1 (1%) fits into 90 :
90/2.1 = 42.85714286...%
that increase from $210 to $300 was 42.85714286...%.
an additional $50 baggage fee ?
we have to add this to the $300 and get $350 as new price.
that difference is now 350 - 210 = $140.
how many % are $140 compared to the original price ?
140/2.1 = 66.66666666...%
that increase from $210 to $350 was 66.66666666...%.
Math question 6 help
f(2)=5_(2^(2))+3_(2+1)
Given this function, what is the output
The value of Function f(x) = 5x²+ 3x + 1 at x=2 is 27.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
Given:
We have the Function as
f(x) = 5x²+ 3x + 1
Now, we have to find value of function at x= 2 so
f(x) = 5x²+ 3x + 1
f(2) = 5(2)²+ 3(2) + 1
f(2) = 5(4)+ 6 + 1
f(2) = 20 + 7
f(2)= 27
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I NEED HELP AND FAST
Answer:
-1 ⇒ -6
0 ⇒ -2
1 ⇒ 2
2⇒6
Step-by-step explanation:
An equivalent expression for (3x+2)/(x-5) with a denominator of (3x+4)(x-5) can be ob
we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:
(3x + 2)(x - 5) / (3x + 4)(x - 5) = (3x + 2)/(3x + 4)
To obtain an equivalent expression for (3x+2)/(x-5) with a denominator of (3x+4)(x-5), we can use the distributive property to expand the numerator and denominator:
(3x + 2) / (x - 5) = (3x + 2)(x - 5) / (3x + 4)(x - 5)
From here, we can use the fact that anything multiplied by 1 results in the same value to simplify the expression:
(3x + 2)(x - 5) / (3x + 4)(x - 5) = (3x + 2)/(3x + 4)
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What is the equation of the midline of the sinusoidal function?
Enter your answer in the box.
y =
The equation of the midline of the sinusoidal function will be y = 4.
What is a sinusoidal Function?The most obvious representation of the amount that objects, in reality, modify their state is a sinusoidal waveform or sinusoidal wave. A sine wave depicts how the intensity of a variable varies over time. For example, the variable may be an audible sound.
The sinusoidal equation is written as,
y = A sin (ωt + ∅) + k
Here, 'A' is the amplitude, 'ω' is the frequency, and '∅' is the phase difference.
From the graph, it can be seen that the function is shifted upward by four units. Then the equation of the midline of the sine function is given as,
y = 4
The equation of the midline of the sinusoidal function will be y = 4.
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B Solve the following showing all steps \( 5 \quad \log _{2}(32)=x \) \( 6 \log _{2}(x-4)+\log _{2}(x)=5 \)
To solve this problem, use logarithmic properties to combine the two equations into one.
First, use the product rule to combine the two equations:
$\log_2(32) + \log_2(x-4) + \log_2(x) = 5$
Then use the power rule to combine the last two terms:
$\log_2(32) + \log_2(x^2 - 4x) = 5$
Finally, use the quotient rule to separate the terms:
$\log_2\frac{32}{x^2 - 4x} = 5$
To solve for $x$, take the inverse logarithm of both sides:
$\frac{32}{x^2 - 4x} = 2^5$
Expand and simplify the left side to get a quadratic equation:
$x^2 - 4x - 32 = 0$
Solve the quadratic equation using the quadratic formula:
$x = \frac{4 \pm \sqrt{4^2 + 4(32)}}{2}$
$x = \frac{4 \pm \sqrt{136}}{2}$
$x = 4 \pm \sqrt{17}$
Therefore, the solutions are:
$x = 4 + \sqrt{17}$
$x = 4 - \sqrt{17}$
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HELP! i dont know what to do pls help
tiplication an(d)/(o)r division on the rational expressions ano (x^(2)-3x-18)/(x^(2)+10x+21)-:(x^(2)+3x-54)/(x^(2)-x-30)*(x^(2)+16x+63)/(x^(2)+14x+45)
The simplified rational expression is (x³-6x²+5x²)-30x+5x²-30x+25x-150)/(x³+17x²+75x+175)
To simplify the rational expression, we will need to use multiplication and division of the rational expressions. We will also need to factor the expressions in order to simplify them.
First, let's factor the expressions:
(x²-3x-18)/(x²+10x+21)-:(x²+3x-54)/(x²-x-30)*(x²+16x+63)/(x²+14x+45)
= ((x-6)(x+3))/((x+7)(x+3))-:((x+9)(x-6))/((x-6)(x+5))*((x+9)(x+7))/((x+9)(x+5))
Next, let's simplify the expressions by canceling out the common factors:
= (x-6)/(x+7)-: (x+9)/(x+5)*(x+7)/(x+5)
= (x-6)/(x+7)-: (x+9)(x+7)/(x+5)(x+5)
Now, let's multiply the expressions:
= (x-6)(x+5)(x+5)/(x+7)(x+5)(x+5) - (x+9)(x+7)(x+7)/(x+7)(x+5)(x+5)
Finally, let's subtract the expressions:
= ((x-6)(x+5)(x+5) - (x+9)(x+7)(x+7))/((x+7)(x+5)(x+5))
= (x³-6x²+5x²-30x+5x²-30x+25x-150)/(x²+17x²+75x+175)
Therefore, the simplified rational expression is:
= (x³-6x²+5x²-30x+5x²-30x+25x-150)/(x³+17x²+75x+175)
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Malcolm is finding the solutions of this quadratic equation by factoring
3r²-24x=-45
Which of these is a correctly factored equation that can be used to find the solutions?
O 3(2-15)(x+1)=0
O 3(x-3)(x-5)=0
○ (3x - 5)(+9) = 0
O (3-3)(r-15) = 0
In a case whereby Malcolm is finding the solutions of this quadratic equation by factoring 3x²-24x=-45, the correctly factored equation that can be used to find the solutions is 3(x-3)(x-5)=0
How can the solution be found?The given equation is 3x²-24x=-45
The equation can be re written as;
3x²-24x=-45
3x²-24x+45 = 0
Then we can divide by 3 and have
x²-8x + 12= 0
thene if we factorize we have
x= 5, x= 3
Therefore, option B is correct. which is 3(x-3)(x-5)=0
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Assume we can move the hour and minute hands on a clock freely. Find the measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1. (Note: There are 360° in a circle. Use the measure of the angle that is less than or equal to 180°.)
The measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1 is 144°.
To find the measure of the angle that is created when we move the hour hand to 5 and the minute hand to 1, we need to calculate the difference between the two positions on the clock.
Each hour on the clock represents (360°/12) = 30°, and each minute represents (360°/60) = 6°.
Therefore, the hour hand at 5 represents 150° (5 x 30°) and the minute hand at 1 represents 6° (1 x 6°). The difference between the two positions is 144° (150° - 6°).
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Find all values of m for which the equation has two complex (non-real ) solutions.
The answer of values of m for which the equation has two complex (non-real) solutions are all values greater than 1/8. In other words, m > 1/8
To find all values of m for which the equation has two complex (non-real) solutions, we need to use the discriminant of the quadratic formula.
The discriminant is the part of the quadratic formula under the square root: b²-4ac. If the discriminant is less than 0, then the equation will have two complex (non-real) solutions.
So, let's start by setting the discriminant to be less than 0:
b²-4ac < 0
Now, let's plug in the values from the equation into the discriminant. The equation is in the form ax²+bx+c=0, so we can plug in the values for a, b, and c:
(1)²-4(m)(2) < 0
Simplify:
1-8m < 0
Subtract 1 from both sides:
-8m < -1
Divide both sides by -8:
m > 1/8
So, the values of m for which the equation has two complex (non-real) solutions are all values greater than 1/8. In other words, m > 1/8.
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Allister’s father is 120% of Allister’s height. If his father measures 180 cm, then how many centimeters tall is Allister? help plsss
Answer:
Step-by-step explanation:
216
Test the hypothesis that a majority of the population of soft drink consumers prefer pepsi over coke. Use alpha=.10 (define the population parameter in H0)
Test the hypothesis that a majority of the population of soft drink consumers prefer pepsi over coke. Use alpha=.10 (define the population parameter in H0)
H0:
Ha:
Test statistic:
Rejection Region:
Obtain the P value:
Conclusion:
a)z-score
b)z-score > 1.64
c)comparing the z-score to a z-table
d)a majority of the population of soft drink consumers prefer Pepsi over Coke.
To test the hypothesis that a majority of the population of soft drink consumers prefer Pepsi over Coke, we will use a significance level of α = .10.
H0: The proportion of soft drink consumers who prefer Pepsi is ≤ 0.5.
Ha: The proportion of soft drink consumers who prefer Pepsi is > 0.5.
Test statistic: z-score
Rejection Region: z-score > 1.64
We will obtain the P value by comparing the z-score to a z-table.
Conclusion: Based on the P value, if it is less than or equal to the significance level of 0.10, then we reject the null hypothesis. We can conclude that there is sufficient evidence to suggest that a majority of the population of soft drink consumers prefer Pepsi over Coke.
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