Answer:
Volume of the rectangular prism is [tex]11\frac{1}{4}[/tex] cubic feet.
The number of small cubes required is 90.
Step-by-step explanation:
The rectangular prism has a length of [tex]2\frac{1}{2}[/tex] feet, a width of 3 feet, and a height of [tex]1\frac{1}{2}[/tex] feet.
Now, the volume of the rectangular prism will be [tex](2\frac{1}{2} \times 3 \times 1\frac{1}{2}) = (\frac{5}{2} \times 3 \times \frac{3}{2}) = \frac{45}{4}[/tex] cubic feet i.e. [tex]11\frac{1}{4}[/tex] cubic feet. (Answer)
Now, the volume of the small unit cubes of side lengths of [tex]\frac{1}{2}[/tex] feet will be [tex](\frac{1}{2})^{3} = \frac{1}{8}[/tex] cubic feet.
So, the number of small cubes required to fill the large cube will be [tex](\frac{45}{4} \div \frac{1}{8}) = 90[/tex]. (Answer)
Stuck on this please help
Answer:
The answers are given below.
Step-by-step explanation:
7. Simplified Fractions/Integers:
a. [tex]$ (25)^{\frac{-3}{2}} $[/tex]
= [tex]$ (5^2)^{\frac{-3}{2}} $[/tex]
= [tex]$ 5^{-3} $[/tex]
= [tex]$ \frac{1}{5^3} = \frac{1}{125} $[/tex] is the required answer.
b. [tex]$ \bigg ( \frac{1}{7} \bigg )^{2} $[/tex]
= [tex]$ \bigg( \frac{1}{7^2} \bigg) $[/tex]
= [tex]$ \frac{1}{49} $[/tex] is the required answer.
c. [tex]$ \bigg ( \frac{1}{7} \bigg) ^{-3} $[/tex]
= [tex]$ \bigg ( \frac{1}{7^{-3}} \bigg )$[/tex]
= [tex]$ 7^{3} $[/tex] = 343 is the required answer.
8. Simplified Fractions:
a. [tex]$ \bigg( \frac{27}{8} \bigg ) ^{\frac{2}{3}}$[/tex]
= [tex]$ \bigg ( \frac{3^3}{2^3} \bigg ) ^{\frac{2}{3}} $[/tex]
= [tex]$ \bigg ( \frac{3}{2} \bigg) ^2 $[/tex]
[tex]$ = \frac{9}{4} $[/tex] is the required answer.
b. [tex]$ \bigg ( \frac{4}{25} \bigg)^{\frac{-3}{2}} $[/tex]
= [tex]$ \bigg ( \frac{2^2}{5^2} \bigg)^{\frac{-3}{2}}[/tex]
= [tex]$ \bigg ( \frac{2^{-3}}{5^{-3}} \bigg ) $[/tex]
= [tex]$ \bigg( \frac{5^3}{2^3} \bigg ) $[/tex]
= [tex]$ \frac{125}{8} $[/tex] is the required answer.
9. Index Forms:
a. √3
= [tex]$ 3^{\frac{1}{2}} $[/tex] is the required answer.
b. ∛3
= [tex]$ 3^{\frac{1}{3}} $[/tex] is the required answer.
c. [tex]$\sqrt[6]{2} $[/tex]
= [tex]$ 2^{\frac{1}{6} $[/tex] is the required answer.
d. [tex]$ \sqrt{5^3} $[/tex]
= [tex]$ 5^{\frac{3}{2}} $[/tex] is the required answer.
e. [tex]$ \frac{1}{(\sqrt[3]{5})^2} $[/tex]
= [tex]$ \frac{1}{5^{\frac{2}{3}}} $[/tex]
= [tex]$ 5^{\frac{-2}{3}} $[/tex] is the required answer.
I need help on this question someone plz help me
Answer:
The slopes of the lines are different.
Step-by-step explanation:
If you do convert the standard form equation to slope-intercept form, you get ...
y = -x +5
You see that the slope of this line is -1, whereas the slope of the other line is +1. Both lines have a y-intercept of 5. It is the slopes that are different.
_____
You can determine this to be the case without converting the form of the equation if you have some practice with the various forms of the equation of a line.
In standard form, if the variable signs are the same, the slope is negative. Of course, in slope-intercept form, the sign of the slope is the sign of the coefficient of x.
Does the data for Camille’s puppy show a function? Why or why not?
Answer: Yes, it does, because each input value has an unique output value.
Step-by-step explanation:
First, you need to know when a relation is considered a function.
By definition, a relation is a function if an only if each input value has one and only one output value.
It is important to remember that the input values are the values of "x" and the output values are the values of "y".
Then, in this case, you can observe in the graph attached ( which shows the data for Camille’s puppy), that each x-value (Weeks) has an unique y-value (Weight in pounds).
Therefore, based on this and keeping on mind the explained before, you can conclude that the data for Camille’s puppy shows a function.
Answer:
Yes it does
Step-by-step explanation:
Because it passes the vertical line test and it only touches 1 unit point in the line no need for big explanations you cant understand
The measure of the supplement of an angle is 12° less than twice the measure of the angle. What is the measurement, in degrees, of the angle and its supplement?
The measurement of the angle is ______ degrees.
The measurement of the supplement is ______ degrees.
Answer:
The measure of the angle is 64 degree.
The measure of the supplement is 116 degree.
Step-by-step explanation:
Let the measure of the angle be 'x'.
Given:
Supplement of the angle is 12 less than twice the measure of the angle.
Twice the angle means 2 times of the angle which is [tex]2x[/tex] and 12 less means 12 is subtracted from [tex]2x[/tex].
So, supplement of the angle = [tex]2x-12[/tex]
Now, by definition of supplementary angles, if two angles are supplement of one another, then their sum is 180 degrees.
Therefore, the sum of the given angles = 180°
⇒ [tex]x+2x-12=180[/tex]
⇒ [tex]3x-12=180[/tex]
⇒ [tex]3x=180+12[/tex]
⇒ [tex]3x=192[/tex]
⇒ [tex]x=\frac{192}{3}=64\°[/tex]
The measure of the supplement = [tex]2(64)-12=128-12=116[/tex]
The measure of the angle is 64 degree.
The measure of the supplement is 116 degree.
3,495 rounded to the nearest thousands
Answer:
The answer is 3000.
Step-by-step explanation:
Start to count from ones->tens->hundreds->thousands (from right to left). When it says nearest thousands, you should look at the previous no. which is in hundreds place. As the no. at hundreds place is lesser than 5, there's nothing to add up. (If no. is greater than 5, you should add 1 to the thousands place)
How do you solve 3/4x=-24
Answer:
x = -32
Step-by-step explanation:
¾ x = -24
Multiply both sides by 4.
3x = -96
Divide both sides by 3.
x = -32
Answer:
x = -2
Step-by-step explanation:
Divide -24 by 3 = -8
4x=-8
Divide -8 by 4 = -2
x = -2
0.00035 + (4.2 x 10-5)
Step-by-step explanation:
Solve the bracket first. starting with multiplication and then subtraction
0.00035 + (4.2 x 10-5)
0.00035 + (42-5)
0.00035 + 37
0.01295
On a coordinate grid, AB has an end point B at (24, 16). The midpoint of AB is P(4, -3). What is the y-coordinate of Point A?
The y-coordinate of point A is -22
Step-by-step explanation:
Given
B = (24,16)
P = (4,-3)
The formula for mid-point of AB will be given by:
[tex]P = (\frac{x_A+x_B}{2} , \frac{y_A+y_B}{2})[/tex]
As we already know the y-coordinate of midpoint
We can put the formula's y coordinate equal to the given value
[tex]\frac{y_A+y_B}{2} = -3\\\frac{y_A + 16}{2 } = -3\\y_A+16 = -3 * 2\\y_A +16 = -6\\y_A = -6-16\\y_A = -22[/tex]
Hence,
The y-coordinate of point A is -22
Keywords: Mid-point, coordinate geometry
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The coffee shop is having a special where 2 pounds of coffee cost four dollars. Assume that the total cost in dollars y varies directly with the number of pounds of coffee x. This can be represented by y=2x. How much will 2.5 pounds of coffee cost
Answer:
Step-by-step explanation:
If 2 pounds costs $4, then 1 pound costs $2. That's why the equation is y = 2x and x is the number of pounds you buy. If you buy 2.5 pounds, then the cost is y = 2(2.5) so
y = $5
3. What is the solution to 3x2+3x+5=0? (7 point)
mm -
Cm 2COO
-3+1V17
3
31151
6
-1£i17
2
-3ti51
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Step-by-step explanation:
Given equation is:
[tex]3x^2+3x+5 = 0[/tex]
We will use the quadratic formula for solving the given equation
The quadratic formula is:
[tex]x = \frac{-b+\sqrt{b^2-4ac}}{2a}\ \ \ ,\ \ \ x = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
Here,
a = 3
b = 3
c = 5
[tex]x = \frac{-3+\sqrt{(3)^2-4(3)(5)}}{2(3)}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{(3)^2-4(3)(5)}}{2(3)}\\x = \frac{-3+\sqrt{9-60}}{6}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{9-60}}{6}\\x = \frac{-3+\sqrt{-51}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{-51}}{6}[/tex]
As we know
[tex]i = \sqrt{-1}[/tex]
So,
[tex]x=\frac{-3+\sqrt{51*-1}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{51*-1}}{6}\\x=\frac{-3+(\sqrt{51}*\sqrt{-1})}{6} \ \ \ , \ \ \ \ x = \frac{-3-(\sqrt{51}*\sqrt{-1})}{6}\\x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Hence,
The solution is:
[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]
Keywords: Quadratic equation, quadratic formula
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Find the sum and the difference of the following expressions.
a-b and a+b
The sum is_____, The difference is_____.
Answer:
sum=2a
diff.=-2b
Step-by-step explanation:
a-b+a+b=
2a
a-b-a-b=-2b
Which rule represents an inverse variation?
a. y= x^2
b. y= x/k
c. y= k ⋅ x
d. y ⋅x = k
Answer:
option C. and D.
Step-by-step explanation:
For two quantities with inverse variation, as one quantity increases, the other quantity decreases. For example, when you travel to a particular location, as your speed increases, the time it takes to arrive at that location decreases.An inverse variation can be represented by the equation xy=k or y=kx .
Julian saves 5/7 of the money he makes babysitting. What is 5/7 written as a decimal ?
Answer:
0.714
Step-by-step explanation:
Answer:
0.714...
Step-by-step explanation:
5/7 means 5 divided by 7=
0.71428571...= 0.714(rounded)
Use the equation below to answer the question.
y = 3x + 6
Which equivalent equation is correctly matched with a key feature of the graph of the function it represents?
A
y = 3(x + 2) highlights that the y-intercept is at -2.
y = 3(x + 2) highlights that the y-intercept is at 2.
© y = 3(x + 2) highlights that the x-intercept is at -2.
y = 3(x + 2) highlights that the x-intercept is at 2.
Answer:
The equivalent equation is correctly matched with a key feature of the graph is
y = 3(x + 2) highlights that the x-intercept is at -2.
Step-by-step explanation:
Given:
[tex]y=3x+6[/tex]
Solution:
The Given Equation is in Slope - Point Form i.e
[tex]y=mx+c[/tex]
Where,
[tex]m=slope\\\\c=y-intercept[/tex]
On Comparing the given equation with above we get
[tex]slope=m=3\\\\y-intercept =6[/tex]
Now we Know that
Intercepts:
The line which intersect on x-axis and y-axis are called intercepts.
There are two intercepts:
y-intercept: The line which intersect at y-axis. So when the line intersect at y-axis X coordinate is zero.
x-intercept: The line which intersect at x-axis. So when the line intersect at x-axis Y coordinate is zero.
For x-intercept
Put y = 0 in
[tex]y=3(x+2)[/tex]
[tex]0=3x+6\\\\3x=-6\\\\\therefore x=\dfrac{-6}{3}=-2[/tex]
∴ x-intercept of
[tex]y=3x+6[/tex]
x-intercept = -2
The equivalent equation is correctly matched with a key feature of the graph is
y = 3(x + 2) highlights that the x-intercept is at -2.
Leah has 280 toy cars she puts gift bags of toys together to sell at the flea market. She puts exactly 6 toys in each bag . She only sells full bags of toys. How many full bags of toys can she sell
Final answer:
Leah can make 46 full bags of toy cars to sell at the flea market when placing 6 toys in each bag out of her 280 toy cars, with 4 toys remaining unsold.
Explanation:
Leah has 280 toy cars and wants to sell them in gift bags, with 6 toys in each bag. To find out how many full bags she can sell, we need to divide the total number of toy cars by the number of toys per bag.
The calculation would be 280 ÷ 6 = 46 R4. This means Leah can make 46 full bags of toys and there will be 4 toys left over. Since she only sells full bags, the 4 extra toys will not be sold.
Write down the multiples of 9 between 25 and 50.
Answer:
27, 36, 45Step-by-step explanation:
9×3 = 27
9×4 = 36
9×5 = 45
HOPE IT HELPS
Answer : 9,18,27,36,45,54,63,72,81,90,99,108,117,126,135,144,153,162,171,180,189,198,207,216,225,234,243,252,261,270,279,288,297,306,315,324,333,342,351,360,369,378,387,396,405,414,423,432,441
what is 21.6 rounded to the nearest whole number
Answer:
22
Step-by-step explanation:
21.6 would round up because 6 is closer to 10 than it is 0
The number 21.6 rounded to the nearest whole number is 22.
What is Rounding Off?Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.
Rounding can be done for whole numbers as well as decimals.
Given a number 21.6.
We have to round the number.
Here the first digit after the decimal place is 6, which is greater than 5.
So we have to add 1 to the last digit in the whole part.
So 21.6 is rounded to 22 to the nearest whole number.
Hence the correct number is 22.
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a dozen apples cost$4.92 for a dozen apples is a ratio of what per Apple
Final answer:
Each apple costs 41 cents when a dozen apples are bought for $4.92, determined by dividing the total cost by the number of apples.
Explanation:
The question asks to find the cost per apple when a dozen apples are purchased for $4.92. To find the cost per individual apple, you divide the total cost by the number of apples. There are 12 apples in a dozen, so:
$4.92 ÷ 12 apples = $0.41 per apple
So, each apple costs 41 cents. This exercise of finding the individual cost from a total is an example of a ratio used in basic arithmetic, often taught in middle school mathematics.
Choose as many answers as apply.
Questions you might ask a car dealer include:
Which options are factory installed and which are dealer installed?
Where did you buy that suit?
Is there a dealer advertising fee?
Are there charges for documents like taxes and tags?
Answer:
C,D,A
Step-by-step explanation:
Answer:
Was it factory or dealer-installed?
Are there charges for documents like taxes and tags?
Is there a dealer advertising fee?
Step-by-step explanation:
''Step two involves preparing a list of suitable questions for the dealers you wish to visit. For example, if you want rustproofing, was it factory-installed or dealer-installed? Are there charges for documents like taxes and tags? Is there a dealer advertising fee? These charges won't appear on a factory invoice, but you will pay for them.''
Write the number 110 as a sum of hundred and tens
Answer:
100+10
Step-by-step explanation:
The science club is inflating a model of a hot air balloon. The graph below shows their progress. At what rate is the diameter increasing?
Answer:
12.5 centimeters per minute
Step-by-step explanation:
From the graph, the rate at which the diameter increasing would be inthe units of cm/min
The rate is basically the slope of the line. The slope (m) has formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where
[tex](x_1,y_1)[/tex] is any point from the graph
and
[tex](x_2,y_2)[/tex] is another point from the graph
Let's take the origin (0,0) as the first point and (4,50) as the second point. Now lets calculate the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{50-0}{4-0}\\m=\frac{50}{4}\\m=12.5[/tex]
Thus, we can say:
The diameter of the hot air balloon is increasing at a rate of 12.5 centimeters per minute
the population P of a bacteria culture is modeled by P=4300e^kt, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double?
Answer:
93 h
Step-by-step explanation:
P = 4300eᵏᵗ
1. Calculate the value of k
lnP = ln4300 + kt
ln5800 = ln4300 + k(40 h)
8.666 = 8.366 + 40k h
8.666 - 8.366 = 40k h
0.299 = 40 k h
k= 0.299/40 h = 7.481 × 10⁻³ h⁻¹
2. Calculate the time for the population to double
2 × 4300 = 4300eᵏᵗ
2 = eᵏᵗ
ln2 = kt
t = ln2/k = ln2/(7.481 × 10⁻³ h⁻¹) = 93 h
It takes 93 h for the population to double.
Find the value of X please!!!
Answer:
What are we finding for X?
Step-by-step explanation:
Because the polygons are similar... we can create this proportion relationship.
[tex]\frac{8}{10} = \frac{4}{x}[/tex]
Using cross multiplication...
4·10=8x
8x=40
x=5
answer: x=5
PLEASE HELP HURRY
If you solve an equation by graphing each side as a separate line, which of the following corresponds to the solution of the
equation?
a. there is only a solution if the lines are identical
c. the y-coordinate of the intersection point
b. both the x-coordinate and the y-coordinate of the
d. the x-coordinate of the intersection point
intersection point
Answer:
The x-coordinate gives the solution of the original equation.
Step-by-step explanation:
Let us assume that the original equation is 2x = x + 5 ........... (1) and the solution that this equation has will be x = 5.
But, if we solve the equation by graphing each side as a separate line i.e. y = 2x and y = x + 5, then solving those two equations we get the solution x = 5 and y = 10.
Therefore, the x-coordinate i.e. x = 5 gives the solution of the original equation (1). (Answer)
Answer:
D
Step-by-step explanation:
edge
PLZ HELP I BEG YOU ITS URGENT
James deposited $575 into a bank account that earned 5.5% simple interest each year. If no money was deposited into or withdrawn from the account, how much money was in the account after 2 1/2 years? Round your answer to the nearest cent.
Answer:
$638.25
Step-by-step explanation:
The interest is 5.5% yearly and it is simple interest.
Now, if we consider a deposit of $575 into the bank account that earned 5.5% simple interest each year, then after 2 and half years James will get interest only for 2 years as the 3rd year's interest will be added after the 3rd year.
Therefore, if no money was deposited into or withdrawn from the account, then after 2.5 years the sum will be
[tex]575(1 + \frac{5.5 \times 2}{100}) = 638.25[/tex] dollars. (Answer)
does anyone know to do this
All the information is in the problem you just have to format it into an equation.
Point slope form: [tex]y_{2}-y_{2}=m(x_{2}-x_{1})[/tex] where "m" is the slope.
The equation would look like...
y+6=[tex]\frac{1}{5}[/tex](x+4)
20% of a number is 35 what is the number
Solve for x.
20% × x = 35
0.2x=35
x=175
answer: 175
Answer: 175
Step-by-step explanation: We can change this problem to mean the same thing but it will say 20% of what number is 35.
To answer the question 20% of what number is 35, we translate the question into an equation. First we have 20% which we need to write as a decimal and remember to write 20% as a decimal, we move the decimal point 2 places to the left and we get 0.20.
Next we have "of what number" that's times x, "is 35" = 35. Now we have the equation (.20)(x) = 35.
Not to solve for x, since x is being multiplied by .20, we need to divide by .20 on both sides of the equation. On the left side of the equation the .20's cancel and we have x. On the right side of the equation we have 35 divided by .20 which is 175.
This means that 20% of 175 is 35.
3(9k - 4) - 4(5n - 3) simplify don’t get it
Answer:
27k-20n
Step-by-step explanation:
3(9k-4)-4(5n-3)
27k-12-20n+12
27k-20n-12+12
27k-20n
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y= 8/sqareroot of 2x+4
f(x) = 8, g(x) = square root of quantity two x plus four.
f(x) = square root of quantity two x plus four., g(x) = 8
f(x) = eight divided by x., g(x) = 2x + 4
f(x) = eight divided by square root of x., g(x) = 2x + 4
Answer:
The fourth option gives the result.
Step-by-step explanation:
We have to find f(x) and g(x) from options given such that y = f[g(x)] is equivalent to [tex]y = \frac{8}{\sqrt{2x + 4}}[/tex].
Here, the fourth option gives the result.
If [tex]f(x) = \frac{8}{\sqrt{x} }[/tex] and g(x) = 2x + 4, then the composite function [tex]f[g(x)] = \frac{8}{\sqrt{2x + 4}}[/tex]
⇒ [tex] y = \frac{8}{\sqrt{2x + 4}}[/tex] ( Answer )
A triangular banner has an area of 5ft squared. The height is 3 ft more than the base. Find the base and the
height.
Answer: base a=2ft
height hₐ=5ft
Step-by-step explanation:
use equation for area of triengle
A=a*hₐ/2
hₐ-height of tringle
a-base of triangle
hₐ=a+3
A=a(a+3)/2
2A=a²+3a
A=5ft
2*5=a²+3a
a²+3a-10=0
a=(-3±√9+40)/2
a=(-3±7)/2
a=-5ft
a=2 ft
hₐ=2+3=5ft