[tex]x\geq 3 \ and \ x+1 \geq 4[/tex]
Step-by-step explanation:The question in this problem is:
The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?
First of all, let's name the first variable [tex]x[/tex] which is the smaller number. Accordingly, the lager number will be [tex]x+1[/tex] given that those numbers are consecutive. On the other hand at most conveys the idea of an inequality, which is:
[tex]\leq \\ which \ means \ less \ than[/tex]
So:
1. The sum of 2 consecutive integers can be written as:
[tex]v+(v+1)[/tex]
2. Nine times the smaller and 5 times the larger can be written as:
[tex]9v-5(v+1)[/tex]
Finally, the whole statement:
The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:
[tex]x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ [/tex]
[tex]x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ \frac{6}{2} \leq \frac{2x}{2} \\ \\ 3 \leq x \\ \\ x\geq 3 \\ \\ and \\ \\ x+1 \geq 4[/tex]
The two numbers are:
[tex]x\geq 3 \ and \ x+1 \geq 4[/tex]
What is 2648 to two significant figures?
Answer:
2600 is the significant number.
Step-by-step explanation:
Given : 2648.
To find : What is 2648 to two significant figures.
Solution : We have given 2648.
We can see two last digit are 48 that is less than 50.
To the nearest 100 it become 00
So,2600 is the significant number.
Therefore, 2600 is the significant number.
The number 2648 to two significant figures is 2600
How to determine 2648 to two significant figures?From the question, we have the following parameters that can be used in our computation:
Number = 2648
By definition, the number of significant figures are the digits of a number that are meaningful
Using the above as a guide, we have the following:
Number = 2600 to two significant figures
Hence, the number to two significant figures is 2600
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Which situation will have the greatest number of permutations?
A.
The number of license plates with 4 letters followed by 3 numbers, where letters and digits cannot be repeated.
B.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits cannot be repeated.
C.
The number of license plates with 4 letters followed by 3 numbers, where letters and digits can be repeated.
D.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits can be repeated.
Please select the best answer from the choices provided
A
B
C
D
Answer:
Option C will have greatest number of permutations.
Step-by-step explanation:
A.
The number of license plates with 4 letters followed by 3 numbers, where letters and digits cannot be repeated.
We have total 26 letters (A_Z) and the letters can't be repeated. So we have 26 letter options for 1st letter
25 letters options for 2nd letter
24 letter options for 3rd letter
23 letter options for 4th letter.
So total options for 4 letters 26*25*24*23 = 358800
Now, 3 numbers are required. We have total 10 numbers (0-9)
10 number options for 1st number
9 number options for 2nd number
8 number options for 3rd number
Total options for 3 numbers= 10*9*8 = 720
total options for 4 letters and 3 numbers will be: 358800 * 720 = 258,336,000
B.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits cannot be repeated.
We have total 26 letters (A_Z) and the letters can't be repeated. So we have 26 letter options for 1st letter
25 letters options for 2nd letter
24 letter options for 3rd letter
So total options for 3 letters= 26*25*24 = 15600
Now, 4 numbers are required. We have total 10 numbers (0-9)
10 number options for 1st number
9 number options for 2nd number
8 number options for 3rd number
7 number options for 4th number
Total options for 4 numbers = 10*9*8*7 = 5040
total options for 4 letters and 3 numbers will be: 15600 * 5040 = 78,624,000
C. The number of license plates with 4 letters followed by 3 numbers, where letters and digits can be repeated.
Now, the letters and digits can be repeated. So we have 26 options for each 4 letters and 10 options for each 3 numbers
26*26*26*26 *10*10*10 = 456,976 * 10,00 = 456,976,000
total options for 4 letters and 3 numbers will be: 456,976,000
D.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits can be repeated.
Now, the letters and digits can be repeated. So we have 26 options for each 3 letters and 10 options for each 4 numbers
26*26*26 *10*10*10*10 = 17,576 * 10,000 = 175,760,000
total options for 3 letters and 4 numbers will be: 175,760,000
So, Option C will have greatest number of permutations.
HELP ME , I CANNOT POST PICTURE & I HAVE 2 THINGS THAT REQIRE A PICTURE WHAT DO I DO ??!
Answer:
Step-by-step explanation:
so when you post your picture you wanna click the thing that looks like a paper clip and attach a file or picture. or your can copy your photo and paste it in your question if you dont know how to take a picture just screenshot it *depends what kind of computer your using*
Hello there! I answered a few questions like this before so here is my answer from that question:
- Click "Ask your question."
- Type out the question in the field.
- Click the paperclip icon below the answering field.
- Click "add attachments"
- Select the photo you want to use
- Click "Open" and wait for the photo to load.
There you go! I hope this helped. An easier way to do this is to drag your photo straight into the answer field and you can skip the last 4 steps, I am sure this works on mac but not sure if it works on windows. Have a great day! :)
Melinda earned the following amount of money in tips the past five days at the restaurant: $52, $78, $62, $120, and $71. What was the median amount of money Melinda earned in tips the past five days?
Answer:
The median would be 71
Step-by-step explanation:
The median means middle and 71 is in the middle if you place the numbers in order
Also please drop a brainliest!
Factor x^3+2x^2-9x-18 , given that -2 is a zero.
Answer:
x
3
+
2
x
2
+
9
x
+
18
x3+2x2+9x+18
Factor out the greatest common factor from each group.
Tap for more steps...
x
2
(
x
+
2
)
+
9
(
x
+
2
)
x2(x+2)+9(x+2)
Factor the polynomial by factoring out the greatest common factor,
x
+
2
x+2
.
(
x
+
2
)
(
x
2
+
9
)
(x+2)(x2+9)
Step-by-step explanation:
Answer:
(x + 2)(x + 3)(x - 3)
Step-by-step explanation:
Given that x = - 2 is a zero then (x + 2) is a factor
Dividing x³ + 2x² - 9x - 18 by (x + 2) gives
x³ + 2x² - 9x - 18 = (x + 2)(x² - 9) = (x + 2)(x + 3)(x - 3)
Graph the linear equation.
Y=-1/5x+3
first plot (0,2) then (-1,5)
The graph below is the graph of a function
A. True
B. False
Answer:
false
Step-by-step explanation:
Answer:
A. True
Step-by-step explanation:
Use vertical line test to find our whether the line is the graph of a function or not.
From the photo, we can see that only one output ( value of y) for one input ( value of x) and all vertical lines intersect a curve at most once then the line represents a function.
Hope it will find you well.
line p has an x-intercept of 5 and a y-intercept of 3. Find the slope of line p
Answer:
-3/5
Step-by-step explanation:
you can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope of a line when given two points.
we are given both the x and y intercepts, and we can use those in the formula.
the x intercept is (5,0) and the y intercept is (0,3)
i will treat (5,0) as my x1 and y1, and (0,3) as my x2 and y2
[tex]\frac{3-0}{0-5}[/tex] = -3/5
the slope is -3/5
The slope of the line is -3/5 if the line p has an x-intercept of 5 and a y-intercept of 3.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a line p:
The x-intercept of line p is 5 or (5, 0)
The y-intercept of line p is 3 or (0, 3)
The slope m can be evaluated:
[tex]\rm m =\dfrac{3-0}{0-5}[/tex]
m = -3/5
Thus, the slope of the line is -3/5 if the line p has an x-intercept of 5 and a y-intercept of 3.
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If h(x)=6-x what is the value of (hxh)(10)?
Answer:
16
Step-by-step explanation:
h(x) × h(x) = (6 - x)²
(h × h)(10) = (6 - 10)² = (- 4)² = 16
For this case we have by definition, that given two functions, then:
[tex](f * g) (x) = f (x) + g (x)[/tex]
Here, we want to find ([tex](h * h) (x):[/tex]
[tex](h * h) (x) = (6-x) (6-x)\\(h * h) (x) = 36-6x-6x + x ^ 2\\(h * h) (x) = 36-12x + x ^ 2[/tex]
We want to find the value of the function when [tex]x = 10[/tex].
[tex](h * h) (10) = 36-12 (10) + (10) ^ 2\\(h * h) (10) = 36-120 + 100\\(h * h) (x) = 16[/tex]
Answer:
[tex](h * h) (x) = 16[/tex]
Use complete sentences to describe the domain of the cosine function
The domain of a function is the complete set of possible values of the independent variable.
The cosine function is represented by the expression: y=cos(x), where "x" is the independent function, and "y" the dependent function. So the domain comes to be all the values that "x" can take.
The domain of the cosine function is all the real numbers. All this can be verified by looking at its graph (attached)
I need help on this, what is the ordered pair is a solution?
Answer:
(-2, -1)Step-by-step explanation:
Convert the inequality to the form y > mx + b:
3x + y > -8 subtract 3x from both sides
y > -3x - 8
Put the coordinates of the points to the inequality and check:
for (-3, 0)
0 > -3(-3) - 8 → 0 > 9 - 8 → 0 > 1 FALSE
for (-2, -1)
-1 > -3(-2) - 8 → -1 > 6 - 8 → -1 > -2 TRUE
for (0, -10)
-10 > -3(0) - 8 → -10 > 0 - 8 → -10 > -8 FALSE
for (2, -16)
-16 > -3(2) - 8 → -16 > -6 - 8 → -16 > -14 FALSE
A rock is dropped from a bridge 320 feet above the river. The pathway that the rock takes can be modeled by the equation h= -16t2+320. How long will it take the rock to reach the river?
Answer:
288
Step-by-step explanation:
Answer: 4.47 seconds.
Step-by-step explanation:
Hi, the rock will reach the river when the height (h) is 0.
So, replacing in the equation given:
h= -16t2+320
Where t is the time
0= -16t2+320
Solving for t
-320 = -16t2
-320/-16 =t2
20 = t2
√20 =t
4.47 = t
Assuming that t is the time in seconds, the rock will reach the river after 4.47 seconds.
Feel free to ask for more if needed or if you did not understand something.
Which of the following is an example of a variable expense?
Rent
Groceries
Wages
Car insurance
PLEASE HELP!!
Answer:
Step-by-step explanation:
Rent, wages and car insurance don't vary much. Grocery expenses depend upon the particular groceries purchased each time one goes to the grocery store, and are least likely to be steady / constant from week to week.
Which expressions are equivalent to 5+(−3)(6x−5)
Choose all answers that apply:
A
18x−20
B
3x-3
C
None of the above
Answer:
C. None of the aboveStep-by-step explanation:
[tex]5+(-3)(6x-5)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5+(-3)(6x)+(-3)(-5)\\\\=5-18x+15\qquad\text{combine like terms}\\\\=-18x+(5+15)\\\\=-18x+20[/tex]
Answer:
none of the above
Step-by-step explanation:
just for people who dont want one
help with #5 please
729. multiple 9 times 9 then 81 times 9 and you get D
Help me
it an emergency
Answer:
40
Step-by-step explanation:
165% * ? = 66
66 / 165%
66 / (165 / 100)
(100 * 66) / 165
6600 / 165 = 40
what percent of 64 is 16
Answer:
Step-by-step explanation:
The percent of 64 which that is 16 is 25% because, to find what percent a number y is of a number x, you have to follow the steps: Divide y by x.
Answer:
25%
Step-by-step explanation:
The question aks: What percentage of 64 is 16?
Let that percentage be x,
[tex]\frac{x}{100}[/tex] of 64 = 16
We multiply both sides by 100 then divide by 64 to get:
x = [tex]\frac{1600}{64}[/tex] = 25%
Lily has two times as much money invested in 8% stocks as she has in bonds paying 6%. How much she has invested in stocks if her annual income from stocks and bonds is $325.6?
Answer:
Final answer is $4440.
Step-by-step explanation:
Let amount of money invested in 8% stock = x
Let amount of money invested in 6% stock = y
then total money invested $325.6 gives equation
8% of x + 6% of y = 325.6
0.08x + 0.06y = 325.6
8x + 6y = 32560...(i)
other equation will be x=2y...(ii)
plug (ii) into (i)
8x + 6y = 32560
8(2y) + 6y = 32560
16y+ 6y = 32560
22y = 32560
[tex]y=\frac{32560}{22}[/tex]
y=1480
plug y=1480 into (ii)
x=2y=2(1480)=2960
Then total money invested in stocks = x+y= 1480+2960=4440
Hence final answer is $4440.
Use the following information to find the test statistic of the sample used to test the claim that FICO credit scores are greater than 675. n = 50, = 719, s = 92
t = 32.437
t = –32.437
t = –3.382
t = 3.382
Answer:
t = –3.382
Step-by-step explanation:
Claim: FICO credit scores are greater than 675
Thus, x = 675
We are given:
Sample size = n = 50
Sample Mean = u = 719
Sample Standard deviation = s = 92
The formula to find the t-statistic is:
[tex]t=\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
Using the above values, we get:
[tex]t=\frac{675-719}{\frac{92}{\sqrt{50} } }\\\\ t=-3.382[/tex]
Thus, the value of test statistic is -3.382. So 3rd option gives the correct answer.
Answer:
t = 3.382
Step-by-step explanation:
gradpoint
Nell took out a subsidized student loan of $6000 at a 4.8% APR, compounded
monthly, to pay for her last semester of college. If she will begin paying off
the loan in 10 months with monthly payments lasting for 20 years, what will
be the total amount that she pays in interest on the loan?
A. $9345.60
B. $3345.60
C. $3724.80
D. $9724.80
Answer:
The total interest paid by Nell in 20 years is $3,724.80
C is correct
Step-by-step explanation:
Nell took out a subsidized student loan of $6000 at a 4.8% APR, compounded monthly.
First we find total amount in 10 months
[tex]A=6000(1+\frac{0.048}{12})^{10}[/tex]
[tex]A=6244.37[/tex]
Now, He has to pay loan off on 6244.37 for 20 years at 4.8% APR
Loan Formula:
[tex]P=\dfrac{PV\cdot r}{1-(1+r)^{-n}}[/tex]
PV=6244.37
r=0.048/12
n=240
[tex]P=\dfrac{6244.37\times \frac{0.048}{12}}{1-(1+\frac{0.048}{12})^{-240}}[/tex]
[tex]P=40.52[/tex]
Total pay in 20 years = 40.52 x 20 = 9724.80
Total amount took loan = $6000
Interest = 9724.80 - 6000
= $3,724.80
Hence, The total interest paid by Nell in 20 years is $3,724.80
Answer: $3345.60
Step-by-step explanation:
Apex - Took one for the team on the quiz because I forgot to check the rating on the other answer </3
Solve:
a: 256÷x=64
b: 256÷x=4
c: 36÷d=60
Answer:
x = 4. x = 64, d = 0.60.
Step-by-step explanation:
a. 256 /x = 64
64x = 256
x = 256/64
x = 4.
b. 256/x = 4
4x = 256
x = 256/4
x = 64.
c. 36/d = 60
60d = 36
d = 36/60
d = 0.60.
Need help very badly
Find the area of the yellow region.
Round to the nearest tenth.
Answer:
5.4 ft²
Step-by-step explanation:
Since the circle is inscribed in the square then radius r = 2.5
Area of yellow = area of square - area of circle
A = (5 × 5) - (π × 2.5²)
= 25 - 6.25π ≈ 5.4 ft²
Answer:
Area of the Yellow Region is 5.4 ft²
Step-by-step explanation:
Given:
Length of the side of the square = 5 ft
Diameter of the Circle = Length of the side = 5 ft
⇒ Radius of the circle, r = 5/2 = 2.5 ft
To find: Area of the Yellow region from the figure.
Area of the Yellow Region = Area of the Square - Area of the Circle
= Side × Side - πr²
= 5 × 5 - 3.14 × (2.5)²
= 25 - 3.14 × 6.25
= 25 - 19.625
= 5.375
≈ 5.4 ft² (nearest tenth)
Therefore, Area of the Yellow Region is 5.4 ft²
Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.
If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?
Answer: Obtion B
[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]
Step-by-step explanation:
The equation for exponential decay has the following form:
[tex]y = pe ^{-rt}[/tex]
Where
p is the initial population
r is the rate of decrease
t is time.
In this problem we have to:
The current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million.
So
[tex]p_1 = 1.3[/tex] in millions
[tex]p_2 = 2.1[/tex] in millions
We also need the populations of insect to be reduced at a rate of 3.8% and insect to be reduced at a rate of 4.6%.
so:
[tex]r_1 = 0.038\\\\r_2 = 0.046[/tex]
then the exponential decay equation for insect A is:
[tex]P = 1.3e ^ {-0.038t}[/tex]
the exponential decay equation for insect B is:
[tex]P = 2.1e ^ {-0.046t}[/tex]
Finally, the system of equations is:
[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]
The answer is the Option B
Vertical angles must: check all that apply
Answer:
Have the same vertex , and be congruent.
Step-by-step explanation:
Answer:Have the same vertex , and be congruent.
Step-by-step explanation:
Michael is 25 years younger than his father. The sum of their ages is 53. What is Michael’s age
Answer: 14
Step-by-step explanation:
⇒ Michael's age = x −25
⇒ x − 25 + x = 53
⇒ 2x = 53 + 25
⇒ 2x =78
⇒ x =39
Hence, Michael's age
= x − 25 = 39 − 25 = 14* Hopefully this helps:) Mark me the brainliest:)!!!
~234483279c20~
A spoke of a wheel makes 32 revolutions while the wheel goes 425 feet. Find the approximate radius of the wheel.
Answer:
2.11 ft
Step-by-step explanation:
Given in the question,
number of revolution a wheel make = 32
distance that wheel traveled while rotating = 425ft
Step 1
Find the circumference of the wheel
circumference = total distance covered / number of revolution
= 425 / 32
= 13.28 ft
Step 2
Formula of circumference
2πr = 13.28 ft
r = 13.28/2π
r = 2.11 ft
I need some help with #15
Answer:
B. 1184
Step-by-step explanation:
Answer is B
See photo
Which set of quadrilaterals must have opposite sides that are congruent and parallel?
A.square, rectangle, kite
B.rhombus, rectangle, trapezoid
C.rectangle, parallelogram, rhombus
D.kite, parallelogram, rectangle
Answer:
The answer is option C. rectangle, parallelogram, rhombus
Step-by-step explanation:
The set of quadrilaterals that must have opposite sides that are congruent and parallel are - rectangle, parallelogram, rhombus.
These three quadrilaterals have opposite sides congruent. Kites and trapezoids does not have opposite sides congruent.
The required set of quadrilaterals that satisfy these conditions is a rectangle, parallelogram, and rhombus. Option C is correct.
The set of quadrilaterals that must have opposite sides that are congruent and parallel is option C: rectangle, parallelogram, rhombus.
In a rectangle, opposite sides are congruent and parallel.
In a parallelogram, opposite sides are congruent and parallel.
In a rhombus, opposite sides are congruent and parallel.
Therefore, the set of quadrilaterals that satisfy these conditions is a rectangle, parallelogram, and rhombus. Option C is correct.
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What is the solution to 3|–3x + 9| = –18?
x = –5
x = 5 or x = 1
x = –5 or x = 1
no solution
Answer:
x=5 and x=1
Step-by-step explanation:
3 |-3x + 9| = -18
/3 /3
|-3x + 9| = -6
-3x + 9 = -6 -3x + 9 = 6
-9 -9 -9 -9
-3x = -15 -3x = -3
/-3 /-3 /-3 /-3
x = 5 and x = 1
Answer:
No solution
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
x =
Answer:
25
Step-by-step explanation:
use pythagoras theorem:
sqrt of: a^2+b^2 = c
where
a=24
b=7
c=x
so substitute these values in the theorem:
sqrt: 24^2+7^2=25
hope this helps!
Answer:
25
Step-by-step explanation:
a²+b²+c²
24²+7²=c²
576+49=625
√625=25