Given:
Measure of a cube = 1 unit on each side.
Dimensions of a space 2 units by 3 units by 4 units.
To find:
Number of cubes that can be fit into the given space.
Solution:
The volume of cube is:
[tex]V_1=a^3[/tex]
Where, a is the side length of cube.
[tex]V_1=(1)^3[/tex]
[tex]V_1=1[/tex]
So, the volume of the cube is 1 cubic units.
The volume of the cuboid is:
[tex]V_2=l\times b\times h[/tex]
Where, l is length, w is width and h is height.
Putting [tex]l=2,b=3,h=4[/tex], we get
[tex]V_2=2\times 3\times 4[/tex]
[tex]V_2=24[/tex]
So, the volume of the space is 24 cubic units.
We need to divide the volume of the space by the volume of the cube to find the number of cubes that can be fit into the given space.
[tex]n=\dfrac{V_2}{V_1}[/tex]
[tex]n=\dfrac{24}{1}[/tex]
[tex]n=24[/tex]
Therefore, 24 cubes can be fit into the given space.
In the table, Pattern A uses the rule "add 12" and Pattern B uses the rule "add 3." Pattern A 0 12 24 36 48 Pattern B 0 3 6 9 12 Which statement is true? Every term in Pattern B is 4 times the corresponding term in Pattern A. Every term in Pattern B is 13 the corresponding term in Pattern A. Every term in Pattern B is 9 less than the corresponding term in Pattern A. Every term in Pattern B is 14 the corresponding term in Pattern A.
Answer:
D. Every term in Pattern B is 1/4 the corresponding term in Pattern A.
Step-by-step explanation:
Given
[tex]A:0\ 12\ 24\ 36\ 48[/tex]
[tex]B: 0\ 3\ 6\ 9\ 12[/tex]
Required
The true statement
Option D is true, and the proof is as follows.
The interpretation of D is:
[tex]B = \frac{1}{4}A[/tex]
When [tex]A = 0[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 0 = 0[/tex]
When [tex]A = 12[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 12 = 3[/tex]
When [tex]A = 24[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 24 = 6[/tex]
When [tex]A = 36[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 36 = 9[/tex]
When[tex]A = 48[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 48 = 12[/tex]
Compare the calculated values with the given values of B, we have:
[tex]B: 0\ 3\ 6\ 9\ 12[/tex] --- Calculated
[tex]B: 0\ 3\ 6\ 9\ 12[/tex] --- Given
Hence, (d) is correct
Answer:
d yw
Step-by-step explanation:
i took the test
50points! Select the correct answer.
The function is given by the table of values.
x: 1, 2, 3, 4
f(x): 5, 7, 11, 19,
If f(x) is shifted 5 units down to obtain g(x),
which table of values represents the function g?
A. x: -4, -3, -2, -1
g(x): 0 , 2, 6, 14
B. x: -4, -3, -2, -1
g(x): 5, 7, 11, 19
C. x: 1, 2, 3, 4
g(x): 0, 2, 6, 14
D. x: 1, 2, 3, 4
g(x): 10 , 12, 16, 24
Answer: B
Step-by-step explanation:
its B
The function f(x)= -3x^3 + x^2 +2x rises as x grows very small.
A. True
B. False
False, the function f(x)=[tex]-3x^3 + x^2 +2x[/tex] does not rises as x grows very small.
How to determine the statementFirst, we need to know that functions are described as laws, expressions or rules that are used to show the relationship between two variables in an equation.
These variables are known as;
The independent variableThe dependent variableThe function f(x) =[tex]-3x^3 + x^2 + 2x[/tex] does not rise as x grows very small. When x approaches negative infinity, the dominant term is [tex]-3x^3[/tex], which becomes increasingly negative.
Therefore, the function decreases as x grows very small in the negative direction.
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A salesperson uses random digit dialing to call people and try to interest them in applying for a charge card for a large department store chain. From past experience, she is successful on 2% of her cals. in typical working, she makes 50 calls. Let X be the number of calls on which she is unsuccessful.
a. This is binomial distribution. Explain using the BINS method why this is so.
b. Find the mean and standard deviation of X. Leave answer to 4 d.p
c. Find the probablity of P(X>or equal to 48)
Answer:
a)
In this question, for each call, there are only two possible outcomes, either it is successful, or it is not, so binary outcomes. For each call, the probability of a success or failure is the same, which means that the trials are independent, having the same value of p. And the number of trials, which is 50, is fixed. This means that this is a binomial distribution.
b) The mean is 1 and the standard deviation is 0.9899.
c) [tex]P(X \geq 48) = 0[/tex]
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
From past experience, she is successful on 2% of her calls.
This means that [tex]p = 0.02[/tex]
50 calls.
This means that [tex]n = 50[/tex]
a. This is binomial distribution. Explain using the BINS method why this is so.
BINS: Binary outcomes, Independent Trials, n is fixed, and same value of p for all trials.
In this question, for each call, there are only two possible outcomes, either it is successful, or it is not, so binary outcomes. For each call, the probability of a success or failure is the same, which means that the trials are independent, having the same value of p. And the number of trials, which is 50, is fixed. This means that this is a binomial distribution.
b. Find the mean and standard deviation of X.
The mean is:
[tex]E(X) = np = 50*0.02 = 1[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.02*0.98} = 0.9899[/tex]
The mean is 1 and the standard deviation is 0.9899.
c. Find the probablity of P(X>or equal to 48)
This is:
[tex]P(X \geq 48) = P(X = 48) + P(X = 49) + P(X = 50)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 48) = C_{50,48}.(0.02)^{48}.(0.98)^{2} \approx 0[/tex]
[tex]P(X = 49) = C_{50,49}.(0.02)^{49}.(0.98)^{1} \approx 0[/tex]
[tex]P(X = 50) = C_{50,50}.(0.02)^{50}.(0.98)^{0} \approx 0[/tex]
So
[tex]P(X \geq 48) = 0[/tex]
Find the surface area
Answer:
542.592
Step-by-step explanation:
3.14 x 8 squared + 3.14 x 8 x 13.6
Question 4 of 10 A construction worker needs to put a rectangular window in the side of a building. He knows from measuring that the top and bottom of the window have a width of 5 feet and the sides have a length of 12 feet. He also measured one diagonal to be 13 feat. What is the length of the other diagonal? A. 12 feet B. 17 feet C5 feet D. 13 feet
Answer:
❝ D. 13 feet ❞
Step-by-step explanation:
Here,
Window is in the rectangular shape.Measure of its one diagonal is 13 feet.According to the properties of rectangle,
→ Diagonals of a rectangle are equal.
So, here the length of other diagonal will be 13 feet too.
D. 13 Feet
Step-by-step explanation:
Which ordered pair is not graphed below? Choose 1 answer
Answer:
D. (7, -7)
Step-by-step explanation:
The only coordinates on the coordinate plane are:
(1, 7 ), (-7, 1 ), and (-7, 7).
Your are filling your rectangular hot tub with water. The base is 76 inches by 64 inches. The hot tub hole allons of water. If the hot tub is one-fourth full, what is the approximate height of the water? (5d- Zlinou are filling your rectangular hot tub with water. The base is 76 inches by 64 inches. The hot tub hold allons of water. If the hot tub is one-fourth full, what is the approximate height of the water?
Answer:
1216 inches
Step-by-step explanation:
First you multiply ¼ by 76 times 64
which gives you 1216 inches
Dale has $1,000 to invest. He has a goal to have $2,400 in this investment in 12 years. At what annual rate compounded continuously will Dale reach his goal?
Answer:
9%
Step-by-step explanation:
Given that
The invested amount is $1,000
The future value is $2,400
The time period is 12 years
We need to find out the annual rate that compounded continously
So,
As we know that
Amount = Present value × e^(rate × time)
$2,500 = $1,000 × e^(rate × 12)
2.5 = e^(rate × 12)
ln 2.5 = 10r
ln 2.5 ÷ 10 = r
r = 9%
AP TEST QUESTION 1
PLEASE HELP
ILL GIVE BRAINLIST ANSWER
IMAGE ABOVE
On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
by graphs of the function f (x) and g( x).
[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]
from the graphs n f (x) and g( x) are 1 and 5 .
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If a house has decreased 35% since it was purchased and it currently values 117,000 what was purchase value
Step-by-step explanation:
that means the current value of $117,000 is 100 - 35 = 65% of the original price.
65% = $117,000
1% = 65%/65 = 117000/65 = $1,800
100% = 1%×100 = 1800×100 = $180,000
the original (100%) purchase value was $180,000.
Which sentence is incorrect?
A. -3 > -8
B. -4 > -7
C. -2/5=0.4
D. -5/2=0.4
Answer:
D
Step-by-step explanation:
need help asappppppp
Answer:
what do you need help with
Step-by-step explanation:
in order for me to answer you need to pit the problem
The access code of a garage door consists of 4 digits (0 through 9). All digits can be repeated.
Find the number of possible access codes.
Find the probability of randomly selecting the correct access code on the first try.
Find the probability of not selecting the correct access code on the first try.
Answer:
1
Step-by-step explanation:
a) The number of possible access codes is 1000.
b) The probability of randomly selecting the correct access code on the first try is 1/1000
c) The probability of not selecting the correct access code on the first try is 999/1000.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
a) There are 10 digits from 0 to 9.
First digit= 10 ways
Second digit= 10 ways
Third Digit = 10 ways
Then, possible outcomes
= 10 x 10 x 10
= 1000
b) Exactly 1 out of 1000 codes will be correct
Favorable outcomes= 1
so, probability of randomly selecting the correct access code on the first try
= 1/1000
c) The probability of not selecting the correct access code on the first try.
=1- 1/1000
= 999/1000
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What is the area of the shaded region?
Answer:
[tex] 21.5 \: {cm}^{2} [/tex]
Step-by-step explanation:
Area of the shaded region =Area of square with side 10 cm - Area of circle with radius 5 cm
[tex] = {10}^{2} - 3.14 {(5)}^{2} \\ = 100 - 3.14 \times 25 \\ = 100 - 78.5 \\ = 21.5 \: {cm}^{2} [/tex]
Which cylinder will have a larger volume?
A. 3.5 in
8.5 in
________
B. 2.7 in.
11 in
1. Which of the following is a composite number?
A.47
B. 43
C. 41
D.49
Answer:
D. 49
Step-by-step explanation:
what do we mean by 16 1/4
Answer:
[tex] \sqrt[4]{16} [/tex]
Bridgette has drawn a representation of a sphere with a
radius of 3 units, using the graphs of a circle and an ellipse,
as shown in the picture below on the left.
She needs to determine the equations of the graphs that
will generate the representation of the 3D sphere, as
shown in the picture below on the right.
What are possible equations of the circle and ellipse that
Bridgette can use to create her 3D drawing?
Answer:
C
Step-by-step explanation:
You want the equations of the circle and ellipse in the given figure.
EquationsThe standard form equation for an ellipse is ...
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where 'a' and 'b' are the semi-axes in the x-direction and y-direction, respectively.
You will notice that when a=b=r, the ellipse becomes a circle and the equation can be rewritten as ...
[tex]\dfrac{x^2}{r^2}+\dfrac{y^2}{r^2}=1\ \Longleftrightarrow\ x^2+y^2=r^2[/tex]
ApplicationHere, the radius is 3, the same as the semi-major axis in the x-direction (a=3). The ellipse axis in the y-direction appears to be about 1/3 that value, so b=1, and the equations of the circle and ellipse are ...
[tex]x^2+y^2=9\qquad\text{circle}\\\\\dfrac{x^2}{9}+\dfrac{y^2}{1}=1\qquad\text{ellipse}[/tex]
A combination lock has four wheels in a row. Each wheel has the digits from 0 to 9 on it. How many different combinations are there?
(b)How many different combinations are there if we can only use each digit once?
Answer:
Step-by-step explanation:
a.10^4=10000
b.10×9×8×7=5040
Help me solve solution to the system of equations.
Answer:
[tex](\frac{5}{3} ;\frac{4}{3} ).[/tex]
Step-by-step explanation:
[tex]\left \{ {{x+y=3} \atop {\frac{y+2}{2} =x}} \right. \ = > \ \left \{ {{x+y=3} \atop {y+2=2x}} \right. \ = > \ \left \{ {{x+y=3} \atop {2x-y=2}} \right. \ = > \ \left \{ {{x=\frac{5}{3} } \atop {y=\frac{4}{3} }} \right.[/tex]
Does anyone know?!!!!!
Answer:
units
Step-by-step explanation:
Answer:
Just units
Step-by-step explanation:
The circumference is neither squared nor cubed, and it has to be labeled.
What is the solution to the system of equations?
{x+y=4
{x=y=1
O (3, 1)
O (2, 2)
O (1/2, 3/2)
Answer:
hat are the solution(s) to the system of equations shown below? x2 + y2 = 5 y = 2x. 1) x = 1 and x = −1. 2) x = 1. 3) (1,2)
Step-by-step explanation:
Therefore , the solution of the given problem of linear equation comes out to be (2,2).
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
=> y+ x = 3
=> y= 3-x
=> x= y = 1
=>3-x =1
=> x = 2
=> y = 2
(2,2)
Therefore , the solution of the given problem of linear equation comes out to be (2,2).
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Convert as I dictated
62.9 cg to dekagrams
Xxx
PLEASE HELP
DUE RN
WILL GIVE BRAINLIST
Answer:
0.0629 dg
Step-by-step explanation:
A centigram is a dekagram multiplied by 1000, so dividing 62.9 by 1,000 will get us 0.0629 dg.
PLEASE HELP ME 10 POINTS!!!!! PLEASE
What type of transformation moved the red triangle (rotation, dilation, reflection, translation. Describe the movement in details (how x and Y were changed), give evidence.
Answer:
Translation
Step-by-step explanation:
It only moved, without changing in size, rotating, or being reflected. so its been translated.
What is the approximate circumference of the circle that has a center at (2, 1) and passes through the point (2, 5)?
A.) 8 units
B.) 13 units
C.) 25 units
D.) 50 units
Answer:
C. 25
Step-by-step explanation:
Have a great day!
Set V Is all do you need three digit numbers using the digits 1,2,3,4 and 5. Which set would be considered a subset V
The set that would be considered as subset V = {1,3,5} i.e set of odd numbers
What is a subset?A set A is a subset of another set B if all elements of the set A are elements of the set B. In other words, the set A is contained inside the set B. The subset relationship is denoted as A⊂B. A set is a collection of objects or elements, grouped in the curly braces, such as {a,b,c,d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.
In the set 1,2,3,4,5 contains odd numbers and even numbers. But there are just 2 even numbers and 3 even numbers.
But the subset V of the numbers above must contain 3 numbers, this means that subset V will contain odd numbers from 1 to 5.
Therefore, This means that subset V = { 1,3,5}
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-15 POINTS- only answer if you know, don’t guess.
A. Parallelogram
B. Trapezoid
C. Neither
Answer:
C, neither.
I've attached a picture of what it looks like when you plot it on a graph. As you can see, it is neither. So the answer is C
Hope this helped :)
An Uber company charges $7.50 for the first mile and $1.10 for each additional mile. What is the Uber rate for 9 miles? Use r for the total rate and m for total miles.
Answer:
r = 7.50 + (1.10 × (m - 1))
r = 7.50 + (1.10 × (9 - 1))
r = 16.40
The total uber rate for 9 miles is $16.3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First-mile charge = $7.50
Additional charges after the first mile = $1.10
The total charge for 9 miles.
r = 7.50 + 1.10 x 8
r = 7.50 + 8.8
r = $16.3
Thus,
The total rate for 9 miles is $16.3.
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write the product using exponents. 1/5 x 1/5 x 1/5 x 1/5 x 1/5
Answer: 1/5 with an exponent of 5.
hope this helps :)