The 4-digit positive integers have four different digits where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit is 108.
[tex]5*4*3*1+4*4*3*1=60+28=108[/tex]
Positive integers are the numbers we use to depend: 1,2, 3,4, 1 , 2, three, four, and so forth. Numbers with a fractional component not identical to zero and poor numbers are excluded from a fixed of high-quality integers. The operations of addition, subtraction, multiplication, and division can be finished with tremendous integers.
Positive integers are definitely your counting numbers. wonderful integers are in reality a part of a larger institution of numbers referred to as integers. Integers are all of the whole numbers, each advantageous and poor. by complete numbers, we imply numbers without fractions or decimals.
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We make four cases based on where the multiple of the 5 digits (0 or5) is. The number has to end with either 5 or 0 since it's a multiple of5. In all but the last case, 5 and 0 are used at the end and in another spot that separates the cases.
Case 1: The first digit can't be 0 so it must be 5. There are 4.3 to choose the middle two digits. After that, the last digit has to be 0, so there are a total of 1.4.3.1=12 numbers.
Case 2: The second digit can be 5, leaving 2 choices. The first and third numbers can be chosen in 4.3 ways, like last time. The last digit has to be 0 or 5, but not the one we already used. There are a total of 4.2.3.1=24 numbers.
Case 3: There are the same choices, but the digits 0 and 5 are at the last and second-to-last spots. So there are 4.2.3.1 =24 numbers again.
Case 4: There are 4.3.2 ways to choose the first three numbers. There has to be a 5 in the number because the largest digit is 5. Coincidentally, there are 4.2.3.1 numbers again.
There are a total of 12 + 24.3= (D)84 numbers.
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Determine the equation, in vertex form, for the following parabolas.
A. The graph below
B. has a vertex at (−2, 5) and passes (b) through the point (2, 0)
5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.
We need to determine the equation, in vertex form, for the following parabolas.
How to find the equation, in vertex form?We can find the parabola's equation in vertex form following two steps:
Step 1: Use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)²+k.
Step 2: Find the value of the coefficient a by substituting the coordinates of the point into the equation written in step 1 and solving for a.
Now, substitute (−2, 5) in y=a(x−h)²+k
⇒y=a(x−(-2))²+5
Now, substitute (2, 0) in y=a(x−(-2))²+5.
0=a(2+2)²+5
⇒a=-5/16
So, y=-5/16(x+2)²+5
⇒16y=-5(x²+4x+4)+5
⇒16y=-5x²-20x-20+5
⇒5x²+20x+16y-15=0.
Therefore, 5x²+20x+16y-15=0 is the equation, in vertex form, for the given parabolas.
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The difference of two numbers is 8, and the sum of the squares of these two numbers are 320. what are the numbers
Answer:
There are two sets of numbers that meet the criteria:
1) 8 and 16, or
2) -8 and -16
Step-by-step explanation:
Let's call the two numbers A and B.
We are told:
1) A-B=8, and
2) A^2 + B^2 = 320
Rearrange 1) to solve for A:
A=8+B
Use this value of A in the second equation:
A^2 + B^2 = 320
(8+B)^2 + B^2 = 320
(64+ 16B + B^2) + B^2 = 320
2B^2 + 16B + 64 = 320
B^2 + 8B + 32 = 160
B^2 + 8B + 32 = 160
B^2 + 8B - 128 = 0
(B+16)(B-8)=0
B is either -16 or +8
Assuming B = 8
Then from A-B=8 we find that A = B+8 and A = 16
Does A^2 + B^2 = 320?
(16)^2 + (8)^2 = 320?
256 + 64 = 320? YES
--------------------------------
Assuming B=-16
If B=-16, then from A-B=8 we find that A = 8+(-16) and A = -8
Does A-B=8?
-8 - (-16) = 8? YES
Does A^2 + B^2 = 320?
(-8)^2 + (-16)^2 = 320?
64 + 256 = 320? YES
Which statement about the function is true?
O The function is increasing for all real values of x
where
x<-4.
Answer:
A.) The function is increasing for all real values of x where x < -4
Step-by-step explanation:
On the interval x < -4, all of the x values are increasing. Before x = -4, the line assumes a positive slope because it is heading upwards. After this interval, the function is decreasing because the slope is heading downwards.
On the interval -6 < x < -2, all of the x values are positive because they lie above the x-axis. This does not necessarily mean that all of the values are increasing.
On the interval x < -6 and x > -2, all of the x values are negative because they lie below the x-axis.
Prism A and Prism B have the same volume. Which could be the dimensions of prism B. Please help!
Question : Prism A and Prism B have the same volume. Which could be the dimensions of prism B?
Prism A :
Length = 8 feet
Width = 4 feet
Height = 5 feet
Prism B:
Length = ? feet
Width = ? feet
Height = ? feet
Option 1:
Length = 6 feet
Width = 10 feet
Height = 2 feet
Option 2:
Length = 4 feet
Width = 4 feet
Height = 10 feet
Option 3:
Length = 5 feet
Width = 4 feet
Height = 7 feet
Option 4:
Length = 8 feet
Width = 4 feet
Height = 6 feet
Here, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet.
We know that if the a and b be the length and width of the base respectively and c be the height of a prism, then the volume of the prism is abc.
Given that
length of 1st prism = 8 feet
width of 1st prism = 4 feet
height of 1st prism = 5 feet
So volume of 1st prism = 8 * 4 * 5 = 160 feet³
Now the volume of 1st and 2nd prisms are the same.
So, we have to check the options for length, width, and height of the 2nd prism.
1st option:
Height = 6 feet
Width = 10 feet
Length = 2 feet
So, volume = 6 * 10 * 2 = 120 feet³
Then the 1st option is incorrect.
2nd option:
Height = 4 feet
Width = 4 feet
Length = 10 feet
So, volume = 4 * 4 * 10 = 160 feet³
Then the 2nd option is correct.
Therefore, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet. The 2nd option is correct.
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Consider Mary's experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study
a) If μ₁ is the average learning rate of the 6th graders without background noise level and μ₂ is the average learning rate of the 6th graders with the background noise level
The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.
The null hypothesis, H₀: μ₁ = μ₂
b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.
An alternative hypothesis, Hа: μ₁ ≠ μ₂
c) Assumptions that must be met about the data before she can correctly use an independent t-test
There must be a random selection of the 6th graders
That the two groups are normally similar in their learning abilities
The division of students into the two groups should be at random
d) She has to make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.
She can still get accurate results if she includes some bias in the selection to prove a particular result.
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Find x in the following 45°-45°-90° right triangle. Geometry!!! pls help
Answer:
6
Step-by-step explanation:
The numbering system we commonly use is called the decimal numbering system because it uses ____ symbols to represent all possible numbers.
The numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.
A way of writing numbers is known as a number system.
There are the following number systems:
Decimal number system: "Deci" meaning 10, implies that the number system consists of 10 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.Binary number system: "Bi" meaning 2, implies that the number system consists of 2digits or symbols, namely 0, and 1.Octal number system: "Oct" meaning 8, implies that the number system consists of 8 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, and 8.Hexa-Decimal number system: "Hexa-Deci" meaning 16, implies that the number system consists of 16 symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.
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a property sells for one and a half million dollars. the five owners each receive a fifth of the money.
how much money does each owner receive?
Answer: Each owner gets $300000
Step-by-step explanation:
one and a half million is 1500000
then divide by 5
you get $300000
What word describes the slope of the line passing through points (5, 12) and
(5,-13)?
Answer: undefined
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-13-12}{5-5}[/tex]
[tex]\frac{-25}{0}[/tex]
= undefined
George bought socks for "$"300 and planned to sell them for $6 a pair. write an inequality to find the minimum number of socks he has to sell in order to make a profit of more than 210.
The inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.
In the question, we are given that George bought socks for $300.
Therefore, George's total cost = $300.
We assume the number of pairs of socks George sells to be s.
The unit price per pair quoted by George = $6
Therefore, George's total sales = $6s.
We know that the profit over a transaction is given as the difference between sales and costs, that is,
The profit = The total sales - the total costs,
or, profit = 6s - 300.
In the question, we are required to make a profit of more than 210.
This can be shown by the inequality,
6s - 300 > 210.
Thus, the inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.
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help meee please i need help
Answer:
81pi
Step-by-step explanation:
You are asking yourself the area of pi*r^2 could with r as 9. pi*9^2. solve and you get 81pi :D
A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are
The correct hypothesis that can be set up for this test is given as
H0: mu = 5.8
Ha: mu ≠ 5.8
What is a statistical hypothesis?This is the method of inference that is made in a statistical testing in order to know if the dat available is able to support the claims that have been made.
What the manufacturer wants to know is the average filling of the machine. If it is within 5.8 or not.
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Victoria needs to order some new supplies for the restaurant where she works. The restaurant needs at least 673 glasses. There are currently 368 glasses. If each set on sale contains 10 glasses, write and solve an inequality which can be used to determine x, the number of sets of glasses Victoria could buy for the restaurant to have enough glasses.
Using a linear function, we have that:
The inequality is: [tex]368 + 10x \geq 673[/tex].The solution is: [tex]x \geq 31[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Since there are currently 368 glasses(y-intercept), and each set on sale comes with 10 glasses(slope), the number of glasses after x sales is given by:
y = 368 + 10x.
She needs at least 673 glasses, hence the inequality is:
[tex]y \geq 673[/tex]
[tex]368 + 10x \geq 673[/tex].
Now we solve the inequality to find the number of sets needed:
[tex]10x \geq 305[/tex]
[tex]x \geq 30.5[/tex]
As the number of sets is an integer number, the solution is:
[tex]x \geq 31[/tex].
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Evaluate the function f(x) = − x² + 10x – 6 Find f( -5)
Answer:
f (-5) = -81
Step-by-step explanation:
f (-5) = - (-5)² + 10.(-5) - 6 = -81
Line I is parallel to line M. If the measure of 6 is 75 degrees, what is the measure of 3?
(please look at photo attached)
In the given diagram, the measure of ∠3 will be 105°.
In the given diagram, ∠3 and ∠6 are consecutive interior angles.
How to form supplementary angles by transversal?If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
That is,
∠3 + ∠6 = 180°
From the given information,
∠6 = 75°
Then,
∠3 + 75° = 180°
∠3 = 180° - 75°
∠3 = 105°
Hence, the measure of ∠3 will be 105°.
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Please help!!! What is the slope of a line perpendicular to the following line:
Answer:
b.) 2
Explanation:
Parallel slopes have same slope.
Perpendicular slopes have negatively inverse slope.
[tex]\sf Here \ given \ equation: y = -\dfrac{1}{2} x - 6[/tex]
Comparing it with slope intercept form, "y = mx + b" where m is slope.
Here parallel slope: -1/2
Perpendicular slope: -(-1/2)⁻¹ = 2
What is solve -x+4=x+6
? Question
Kim sells fruit at the farmers market. Her week starts out slow, but she gets much busier later in the week. The sequence that
represents the total kilograms of a fruit she sold the first 4 days of a week is 5, 15, 45, and 135.
Of(n) = 5(3)-1
Of(n) = 3(5)-1
□ f(n) =
(3)"
Of(n) =
(3)"
f(n) = (5)"
E Save &
Identify the explicit and exponential forms of the function, f (n), representing the number of kilograms of fruit sold on the
nth day.
Select all the correct answers.
Submit
Using a geometric sequence, the formula for the number of kilograms of fruit sold on the nth day is:
[tex]f(n) = 5(3)^{n - 1}[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For this problem, the first term and common ratio are given as follows:
[tex]a_1 = 5, q = 3[/tex]
Hence the function can be written as:
[tex]f(n) = 5(3)^{n - 1}[/tex]
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if z varies jointly with x and y when x=3, y=-1, and z=12, what is z when x=-5 and y=6
Step-by-step explanation:
z = 12 = k × 3 × -1
12 = k×-3
-4 = k
z = k× -5×6 = k×-30 = -4 × -30 = 120
An American roulette wheel has 38 slots: two slots are numbered 0 and 00, and the remaining slots are numbered from 1 to 36. Find the probability that the ball lands in an odd-numbered slot. Write your answer as a whole number or reduced fraction.
Answer:
9/19
Step-by-step explanation:
To write the probability as a fraction, put the total number on the bottom and put the number of ways the event can happen, put that on top.
They said there are 38 slots. That's the total, it goes on the bottom.
Landing on an Odd Number is the event we're looking at. There are 18 ways that can happen: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35
That number 18 (bc 18 ways to get an odd number) goes on top.
P(Odd) = 18/38
Always simplify when possible.
18/38
= 9/19
What is the sum of the series infinity e n-1 -3(3/8)^n?
the answer for the question above is 9/5
I don’t understand this, can somebody help?
[tex]not \: penny \: or \: dime = quarter \: or \: nickle[/tex]
[tex]p(x) = \frac{13 + 18}{86} = \frac{31}{86} = 0.36[/tex]
30)[tex]gallons \: for \: car \: 1 = \frac{450}{18} = 25 \: gal[/tex]
[tex]gallons \: for \: car \: 2 = \frac{450}{25} = 18 \: gal[/tex]
[tex]we \: need \: 25 + 18 = 43 \: gallons[/tex]
[tex]43 \times 2.49 = 107.07 \: dollars[/tex]
justification two common tangents
Two common tangents occur when two circles intersect each other at two points.
How to illustrate the information?It should be noted that two common tangents are also referred to as transverse common tangents.
In this case, two common tangents occur when two circles intersect each other at two points.
The diagram is attached.
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Which of the following is a true statement about functions?
Look below at image attached
The true statement about functions is D. If f and g are functions, then (f + g)(-2) = (g + f)(-2).
How to depict the information?It should be noted that a function is used to define the relationship that's exist between rte variables.
In this case, when f and g are functions, then (f + g)(-2) = (g + f)(-2).
Therefore, the correct option is D.
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Each leg of a 45°-45°-90° triangle measures 14 cm. what is the length of the hypotenuse? 7 cm 7 startroot 2 endroot cm 14 cm 14 startroot 2 endroot cm
Answer:
[tex]14\sqrt{2}[/tex]
Step-by-step explanation:
In a 45°-45°-90° triangle, the legs = x and the hypotenuse = [tex]x\sqrt2}[/tex]
x = 14
[tex]x\sqrt{2} =14\sqrt{2}[/tex]
Answer:
d
Step-by-step explanation:
14 startroot 2 endroot cm
A 40 percent discount on a sweater resulted in a saving of $14.40. Find the original price.
Answer:
$36
Step-by-step explanation:
14.40 is 40% of 36.
Answer:
$36
Step-by-step explanation
40/100 = 14.4/?
100 * 14.4 = 1440
1440 / 40 = 36
If an equilateral triangles sides are 8 inches long, what is the height?
I think it’s 8.48 but i’m not sure.
Answer:
6.93
Step-by-step explanation:
formula to find height of equilateral triangle is [tex]\frac{\sqrt{3} }{2} *A[/tex] A is the side of the equilateral triangle
Answer:
6.93 inches
(first option listed)
Step-by-step explanation:
we can find the height of this triangle by turning it into a right triangle, and then using the Pythagorean Theorem
(process shown in photo)
hope this helps!! have a lovely day :)
Triangle G H J is rotated 90 degrees about point X to form triangle S T R.
Triangle GHJ is rotated 90° about point X, resulting in triangle STR. Which congruency statement is true?
TR ≅ GJ
∠S ≅ ∠H
TS ≅ HG
∠R ≅ ∠G
The congruency statement is true TS ≅ HG. so option C is correct.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Given information;
Triangle G H J is rotated 90 degrees about point X to form triangle S T R.
Triangle GHJ is rotated 90° about point X, resulting in triangle STR.
Now, if any triangle is rotated 90 degrees about a point the two sides will be ≅ to each other.
So, ST = GH
RT= HJ
SR= GJ
<S= <G
<T = <H
<R=<J
The side TS ≅ HG.
Hence, option (c) is correct.
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Answer:
C
Step-by-step explanation:
Trust me bro
Select all of the solutions to the equation.
The solution to the equations is; +1/2, -1/2, +√2, and -√2.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
[tex]4x^4 + 7x^2 - 2 = 0\\\\[/tex]
The factored form of the polynomial regression
[tex](4x^2 -1)(x^{2} + 2)[/tex]
So,
[tex](4x^2 -1) = 0\\\\4x^2 = 1\\\\x = \pm \dfrac{1}{2}[/tex]
Also,
[tex](x^{2} + 2) = 0\\\\x^{2} = - 2\\\\x = \pm \sqrt{2}[/tex]
Hence, the solution to the equations are;
+1/2, -1/2, +√2, and -√2.
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Answer:
ABCF
Step-by-step explanation:
how to find volume of a prism
Answer:
- HOW TO FIND VOLUME OF PRISM -
1st step - Write the formula for finding the volume of a regular pentagonal prism. The formula is V = [1/2 x 5 x side x apothem] x height of the prism.
2nd step - Find the area of the pentagonal base face. Let's say the length of a side is 6 cm and the length of the apothem is 7 cm.
3rd step - Find the height. Let's say the height of the shape is 10 cm.
4th step - Multiply the area of the pentagonal base face times the height. ...
and last step - State your answer in cubic units.
Step-by-step explanation:
:):):)