Solve the system of linear equations.
15x - 5y = -20
-3x + y = 4
Answer:
Infinite solutions.
Step-by-step explanation:
Use the elimination method:
15x - 5y = -20
-3x + y = 4 Multiply this equation by 5:
-15x + 5y = 20 Now add this to the first equation:
0 = 0
So the 2 equations are the same and there are infinite solutions.
What does a negative net worth indicate?
a Your assets exceed your liabilities.
b. Your assets equal your liabilities.
C Your liabilities exceed your assets.
d. You have only assets and no liabilities.
Please select the best answer from the choices provided
Answer:
c. Your liabilities exceed your assets.
Step-by-step explanation:
The negative net worth indicates option(C) Your liabilities exceed your assets
What is Negative net worth?This means you owe more money than assets that you own.
What is Liabilities?A liability is something a person or company owes, usually a sum of money
Here,
Negative net worth indicates option (C) Your liabilities exceeds your assets is negative net worth. Because this means you owe more money than assets that you own.
Other options are not indicating negative net worth
Hence, the negative net worth indicates option(C) Your liabilities exceed your assets
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A carnival charges $6 for admission and $2.50 per ride. You have $50 to spend at the carnival. Which of the following inequalities represents the situation if r is the number of rides?
Answer:
[tex]6+2.5r\leq 50[/tex]
Step-by-step explanation:
Hi!
The options regarding the inequalities are not listed, though we can still proceed to write the inequality.
From the problem statement you cannot spend more than $50
and you are charged admission fee of $6 flat
a ride cost $2.50 per ride
the number of rides is given as r
yet in all you must not go beyond your limit
Therefore the inequalities can be presented as
[tex]6+2.5r\leq 50[/tex]
Answer:
2.5r + 6 ≤ 50
Step-by-step explanation:
In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns.a. What is the null and alternative hypothesis?b. What is the test statistic?c. What is the P-value?d. What is the Conclusion?
Answer:
a
The null hypothesis is [tex]H_o : p = 0.75[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.75[/tex]
b
[tex]t = 2.51[/tex]
c
[tex]p-value = 0.01207[/tex]
d
There no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 745[/tex]
The number that said it is morally wrong is [tex]k = 589[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The population proportion is [tex]p = 0.75[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
=> [tex]\r p = \frac{589}{745}[/tex]
=> [tex]\r p = 0.79[/tex]
The null hypothesis is [tex]H_o : p = 0.75[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.75[/tex]
The standard error is mathematically represented as
[tex]SE = \sqrt{\frac{p(1-p)}{n} }[/tex]
=> [tex]SE = \sqrt{\frac{0.75(1-0.75)}{745} }[/tex]
=> [tex]SE =0.0159[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\r p - p }{SE}[/tex]
=> [tex]t = \frac{0.79 - 0.75 }{0.0159}[/tex]
=> [tex]t = 2.51[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(Z > 2.51)[/tex]
From the the z-table
[tex]P(Z > 2.51) = 0.0060366[/tex]
=> [tex]p-value = 2 * 0.0060366[/tex]
=> [tex]p-value = 0.01207[/tex]
From the calculation [tex]p-value >\alpha[/tex]
Hence we fail to reject the null hypothesis
Thus there no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns
3x+8-X=57-4
Is 7 a solution to the question
Answer:
7 is not a solution for x.
Step-by-step explanation:
To see if 7 is a solution for x, we will simply plug in the value for x and see if the left hand side is equal to the right hand side.
3x + 8 - x = 57 - 4
3(7) + 8 - (7) ?= 57 - 4
21 + 8 - 7 ?= 53
29 - 7 ?= 53
22 ?= 53 (( NO ))
Since 22 does not equal 53, 7 is not a solution for x.
Let's find the solution for x:
3x + 8 - x = 57 - 4
2x + 8 = 53
2x = 45
x = 22.5
Let's validate this solution for x:
3x + 8 - (x) = 57 - 4
3(22.5) + 8 - (22.5) ?= 57 - 4
67.5 + 8 - 22.5 ?= 53
45 + 8 ?= 53
53 == 53 (( YES ))
Since 53 is indeed equal to 53, then 22.5 is a solution for x.
Cheers.
Answer:
No, 7 is not a solution. x=11.25
Step-by-step explanation:
To find whether 7 is a solution, we can plug it in as x.
3(7)+8-7=57-4
21+15=53
36=53
No, 7 is not a solution.
We can find the solution by solving out the equation normally
3x+8+x=57-4
2x+8=53
2x=45
x=22.25
Help pleaseeeeee thanks so much
Answer:
The answer is n = 31
Step-by-step explanation:
Equation: 2n + 13 = 75
2n = 75 - 13
2n = 62
n = 62/2
n = 31
check:
2*31 + 13 = 75
62 + 13 = 75
Answer: n = 31
Step-by-step explanation: Remember that the word sum mean addition.
So the sum of twice a number and 13 means 2n + 13 = 75.
So our equation is 2n + 13 = 75.
Now let's solve the equation.
Start by subtracting 13 from both sides to get 2n = 62.
Now, divide both sides by 2 and we have n = 31.
A car, starting from a city, traveled east for 100 km and then west for
130 km. How far from City was the car at the end of the trip?
The limit with the steps if it exist plz
Answer:
1/4
Step-by-step explanation:
Hello, first of all we could say, let 's replace x by 1 and see if we can conclude.
numerator gives [tex]\sqrt{1+15}-4=\sqrt{16}-4=4-4=0[/tex]
denominator gives 1-1=0
So, this is 0/0 and this is not defined.
We need to ask a friend for help. Guillaume de l'Hôpital, French mathematician from the 1600s, has a trick to solve this kind of stuff.
In short, he says that
[tex]\displaystyle \lim_{x\rightarrow c} \ {\dfrac{f(x)}{g(x)}}=\lim_{x\rightarrow c} \ {\dfrac{f'(x)}{g'(x)}}[/tex]
In our case here, we have c = 1
[tex]f(x)=\sqrt{x^2+15}-4\\\\g(x)=x-1[/tex]
[tex]f'(x)=\dfrac{1}{2}\dfrac{2x}{\sqrt{x^2+15}}=\dfrac{x}{\sqrt{x^2+15}}\\\\f'(1)=\dfrac{1}{4}\\\\g'(x)=1\\\\\dfrac{f'(1)}{g'(1)}=\dfrac{1}{4}[/tex]
So, we can conclude
[tex]\displaystyle \lim_{x\rightarrow1} \ {\dfrac{\sqrt{x^2+15}-4}{x-1}}=\lim_{x\rightarrow1} \ {\dfrac{1}{4}}=\boxed{\dfrac{1}{4}}[/tex]
Thanks
How do you do this Please Explain how you did
Answer:
Domain : (- ∞, - 5), and (3 / 2, ∞),
Range : (∞, 0.4437]
Step-by-step explanation:
Assuming that we want our answer in interval notation, let's start by determining the domain. Remember that the domain can be found where the function is undefined.
Given : f(x) = (2x - 7) / (2x² + 7x - 15)
Alternative Form : (2x - 7) / (x + 5)(2x - 3)
To receive this 'alternative form' we can simply factor the expression 2x² + 7x - 15. See the procedure below,
[tex]\mathrm{Given : 2x^2+7x-15} ,[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups : \left(2x^2-3x\right)+\left(10x-15\right)} ,[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right),\\\mathrm{Factor\:out\:}5\mathrm{\:from\:}10x-15\mathrm{:\quad }5\left(2x-3\right),[/tex]
[tex]x\left(2x-3\right)+5\left(2x-3\right) = \left(2x-3\right)\left(x+5\right) - \mathrm{Factored\:expression}[/tex]
Now let's find the domain using the expression '(x + 5)(2x - 3) = 0.' If the denominator equals 0, the function is considered undefined.
[tex]\mathrm{Given : \left(x+5\right)\left(2x-3\right)=0} ,\\x+5=0:\quad x=-5, 2x-3=0:\quad x=\frac{3}{2}\\\mathrm{The\:solutions\:are: x=-5,\:x=\frac{3}{2}}[/tex]
Knowing these solutions the domain has the intervals (- ∞, - 5), and (3 / 2, ∞). The range is the set of values that correspond to the domain, so in this case the range would be (∞, 42 + 8√17 / 169]. 42 + 8√17 / 169 = (About) 0.4437, so it lies on the interval (∞, 0.4437].
The images below represent the plotted function in two areas. There are 3 curves in this graph.
If the population does not follow the normal probability distribution, the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size. In most cases, sample sizes of 5 or more will result in sample means being normally distributed, regardless of the shape of the population distribution.a) trueb) false
Answer:
The correct option is false
Step-by-step explanation:
Generally the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size( i.e [tex]n \ge 30[/tex] ) regardless of the shape of the population distribution.
But the question states that the mean is normally distributed if the sample size is 5 or more which is false hence the statement is false
Need help Bad sow work need that to 1. Megan works at Amazon’s warehouse. She is responsible for packing boxes into crates for shipment. Each crate can hold 32 boxes, and she needs to ship 712 boxes. a. Megan thinks she can fit all 712 boxes into 22 crates. Is her estimate correct? Why or why not? EXPLAIN YOUR REASONING b. How many crates will Megan need to pack all 712 boxes? Round to the nearest whole number. SHOW YOUR WORK
Answer:
a) her estimate is wrong, because 22 crates can only contain 704 boxes
b) 23 crates
Step-by-step explanation:
Each crate can hold 32 boxes and there are total of 712 boxes.
Megan thinks she can fit all 712 boxes into 22 crates.
Now multiplying 22 crates 32 boxes to know the number of boxes22 crates can contain
= 22*32
= 704 boxes
The boxes are not all contacts in 22 crates
To pack 712 boxes
She Will need = 712/32 crates
She will need= 22.25 crates
Rounding up to whole number she will need 23 crates
What percent of students in a distribution falls between the first and third quartiles?A) Approximately 25% B) Approximately 50%.C) Approximately 75%.D) Approximately 100%.
Answer:
B) Approximately 50%
Step-by-step explanation:
In any distribution of data, the data can be divided into 4 main quarters that are approximately equal in percentage.
Thus, the first quartile consists of approximately 25%, the second is 25%, third quartile about 25%, while the fourth is 25% also.
Therefore, in a data set distribution of students, approximately 50% of the distribution of students will fall within the first and third quartiles.
Answer:
(B) Approximately 50%
Step-by-step explanation:
First quartile is 1/4 and that is 25% of students in the distribution.
Third quartile is 3/4 and that is 75% of students in the distribution.
Between the first quartile and third quartile is automatically, 50% of the students in the distribution. The answer is (B) Approximately 50%.
f(x) = 6x² + 3x + 2 and g(x) = x - 7
Find f(x) * g(x)
Answer:
work shown and pictured
what are the size of a penny
Answer:
0.75 inches is the correct answer
Answer:
0.75 inches
The coin is 0.75 inches (19.05 mm) in diameter and 0.0598 inches (1.52 mm) in thickness.
-Russell wants to buy three identical gift cards. hehe wants to make sure his total cost is no more than $2 above or below $60. which of the following inequalities represent his situation
Answer:
|60+3c|<2
That should be a less than or equal to sign
Also I’m sorry but I can’t explain it because I got this answer from someone else on here.
Step-by-step explanation:
Need Help on this Part
To determine the 'intervals of increase' and 'intervals of decrease' we can refer to the graph with respect to the x - axis.
• Knowing that t = x - axis, the 'intervals of increase' as an inequality would be 1 < x < 3, and 4 < x < ∞. Therefore we have our intervals of increase as (1,3) and (4, ∞).
• Respectively our 'intervals of decrease' as inequalities would be - ∞ < x < 1, and 3 < x < 4. Our intervals of decrease would then be (- ∞, 1) and (3,4).
• We are left with our local extrema and absolute extrema. Now remember the absolute extrema is the absolute lowest point in the whole graph, while the local extrema is the lowest point in a restricted interval. In this case our local extrema is our maximum, (3,1). But this maximum is not greater than the starting point (0, 4) so it appears, and hence their is no absolute extrema.
f(x) = 4x + 1 and g(x) = 4x - 3
Find f(x) * g(x)
Answer:
16x^2 - 8x - 3
Step-by-step explanation:
f(x) = 4x + 1
g(x) = 4x -3
f(x) * g(x) = (4x+1) * (4x-3)
(16x^2 - 12x + 4x -3)
Combine like terms
16x^2 - 8x - 3
that's your answer
The value of f (x) × g (x) will be;
⇒ 16x² - 8x - 3
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The value of function are,
⇒ f(x) = 4x + 1
⇒ g (x) = 4x - 3
Now.
Since, The value of function are,
⇒ f(x) = 4x + 1
⇒ g (x) = 4x - 3
Hence, We get;
⇒ f (x) × g (x) = (4x + 1) (4x - 3)
= 16x² - 12x + 4x - 3
= 16x² - 8x - 3
Thus, The value of f (x) × g (x) = (16x² - 8x - 3)
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Solve for k 8k-2z=24
Answer:
k = z/4 + 3
Step-by-step explanation:
8k-2z = 24
8k = 24 + 2z
k = (24 + 2z)/8
k = (24 + 2z) / (4*2)
k = (12 + z) / 4
k = 3 + z/4
An ancient culture labeled certain numbers as square numbers. The numbers 1, 4, 9, 16, 25, and so on are square numbers. Complete parts a through c below. . . . .
1 4 16 25 36, 49, 64
Describe a procedure to determine the next five square numbers without drawing the figures.
A. Square 6, 8, 10, 12, and 14.
B. Add the last two square numbers together to get the next one.
C. Double the previous square number and then subtract half of the previous from that.
D. Square 6, 7, 8, 9 and 10.
Answer:
A. 6 = 36
8 = 64
10 = 100
12 = 144
14 = 196
B. 340
C. 582
D.6= 36
7 =49
8 = 64
9= 81
10= 100
Evaluate the expression (q/p)+3p^2 if q=3.5 and p=1
Answer:
The answer is 6.5
Step-by-step explanation:
(3.5/1)+3(1)^2
3.5/1=3.5
3(1)^2=3
3.5+3=6.5
x + y = 12 and y = x - 1.
Find the value of 2x + 2y.
Answer:
2x + 2y = 24
Step-by-step explanation:
You have to isolate y and then use substitution.
x + y = 12 and y = x - 1
-x -x
y = -x + 12 and y = x - 1
-x + 12 = x - 1
+x +x
--------------------
12 = 2x - 1
+1 +1
----------------
13 = 2x
2x = 13 [ divide both sides by 2]
x = 6.5
Now, you have to plug x (6.5) into y = x - 1.
y = x - 1
y = 6.5 - 1
y = 5.5
Finally, plug both x (6.5) and y (5.5) into 2x + 2y.
2x + 2y
= 2 (6.5) + 2 (5.5)
= 13 + 11
= 24
Do you need to execute the Distributive Property to simplify: 5(2-8)?
Yes
No
no just do the stuff in the parentheses then multiply by 5
Solve for x in the diagram below.
Answer:
x= 20
Step-by-step explanation:
The two smaller angles add to 90 degrees
x + 3x +10 = 90
4x+10 = 90
Subtract 10 from each side
4x+10-10 = 90-10
4x = 80
Divide each side by 4
4x/4 = 80/4
x = 20
Answer:
[tex]x=20\textdegree[/tex]
Step-by-step explanation:
The angle we have here is a right angle. Right angles have a total measure of 90°. Therefore, the two parts must equal 90°:
Thus, we have the equation:
[tex](x)+(3x+10)=90[/tex]
Combine like terms:
[tex]4x+10=90[/tex]
Subtract 10 from both sides. The left side cancels:
[tex](4x+10)-10=90-10\\4x=80[/tex]
Divide both sides by 4. The left side cancels:
[tex](4x)/4=(80)/4\\x=20[/tex]
Thus, x is 20°.
what do 16 and 24 have in common
Answer:
both are positive even composite integers with a common factor of 8.
Step-by-step explanation:
Both are positive even composite integers with a common factor of 8. They are solutions to the quadratic equation (x-16)(x-24) = 0. Their cube roots (or any root of index greater than 2) are irrational. They are divisors of 48.
There are also many things that both numbers are not. They are not the lengths of sides of a right triangle with integer side lengths. They are not negative or irrational. They are not triangle numbers or elements of the Fibonacci sequence.
Why is it important to line up the decimal points?
2. True False 6(10 + 5) - 6.10 + 6.5
[tex]10 + 5 - 6.10 + 6.5 \times 6[/tex]
Answer:
47.9Step-by-step explanation:
[tex]10 + 5 - 6.10 + 6.5 \times 6 \\ [/tex]
Follow PEDMAS
[tex]10 + 5 - 6.10 + 39[/tex]
[tex]15 - 6.10 + 39 \\ 15 + 39 - 6.10 \\ 54 - 6.10 \\ = 47.9[/tex]
What number is greater then -8 and less than 0?
Answer: -9 and up
Step-by-step explanation: An integer is any whole number. An integer can be zero, greater than zero or less than zero. The integers greater than zero are the natural numbers.
Answer:
-7 through -1
Step-by-step explanation:
its more than -8 and less than 0 i had this question in 7th yr
Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).
Answer:
Rate of change = 18/√74
Step-by-step explanation:
The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v
Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;
∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)
So;
∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))
This gives;
∇g(1, 1, 2) = (3, 7, 4)
Now,
||∇g(1, 1, 2)|| = √(3² + 7² + 4²)
||∇g(1, 1, 2)|| = √74
Normal vector would be given by the formula;
v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]
Thus;
v = (3, 7, 4)/√74
Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)
Thus, rate of change is given by;
∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74
This gives;
Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74
Solve:(1/7)x +(1/6)y =3 ; (1/2)x - (1/3)y =5
Answer:
(14, 6 )
Step-by-step explanation:
Given
[tex]\frac{1}{7}[/tex] x + [tex]\frac{1}{6}[/tex] y = 3 ( multiply through by 42 to clear the fractions )
6x + 7y = 126 → (1)
[tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{3}[/tex] y = 5 ( multiply through by 6 to clear the fractions )
3x - 2y = 30 → (2)
Multiplying (2) by - 2 and adding to (1) will eliminate the x- term
- 6x + 4y = - 60 → (3)
Add (1) and (3)term by term to eliminate x
11y = 66 ( divide both sides by 11 )
y = 6
Substitute y = 6 into either of the 2 equations and evaluate for x
Substituting into (1)
6x + 7(6) = 126
6x + 42 = 126 ( subtract 42 from both sides )
6x = 84 ( divide both sides by 6 )
x = 14
Solution is (14, 6 )
in the first quadrant you start at is (1,4)d move 4 units right what is the point
Answer:
(5,4)
Step-by-step explanation:
Moving right, so moving along the x- axis in the positive direction. So add 4 to the x value of the ordered pair.