Answer:
The first equation can be multiplied by 3 and the second equation by 2.
Step-by-step explanation:
We are given the following system of equations:
[tex]\boxed{\left \{ {{2x+3y=25} \atop {-3x+4y=22}} \right.}[/tex]
To eliminate a variable in the equation, they must cancel out. For instance, if x = 1, in order to cancel out the numbers, you must add -1.
To multiply an equation, you must apply the constant that you are multiplying by to all constants and coefficients of the equation. For example, to multiply 2x + 4y = 8 by 3, you must multiply 2x by 3, 4y by 3, and 8 by 3.
Therefore, using this information, you can attempt each answer set and test the possibilities.
Answer Choice A
If you multiply the first equation by -3, you will get -6x - 9y = -75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -6 + -6 gives you -12, so these do not cancel out.
Answer Choice B
If you multiply the first equation by -4, you will get -8x - 12y = -100. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -8 + -6 gives you -14, so these do not cancel out.
Answer Choice C
If you multiply the first equation by 3, you will get 6x + 9y = 75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding 6 + -6 gives you 0, so these do cancel out.
Answer Choice D
If you multiply the first equation by 4, you will get 8x + 12y = 100. If you multiply the second equation by -3, you will get 9x - 12y = -66. Adding 8 + -9 gives you -1, so these do not cancel out.
Find an equation of the vertical line passing through the point (-4, 2). x=
Answer:
x = -4
Step-by-step explanation:
This vertical line is x = -4. That's all we need here.
-3=9(5-2k)/5 Show your work
Answer:
K=3.333
Step-by-step explanation:
-3=9(5-2k)/5
-3=45-18k/5
-15=45-18k
18k=60
K=60/18
K=3.3333
a. Is the a discrete random variable, a continuous random variable, or not a random variable? amount of rain in City B during April A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
Answer:
The correct answer is:
It is a continuous random variable. (B)
Step-by-step explanation:
Continuous random variables are variables that take on infinite possibility of values, hence the number of possible outcomes of a random variable cannot be counted. For instance, in this example, the amount of rainfall measured using a rain guage or a pluviometer has infinite possibilities of outcomes. it can either be 22.3 Liters, 20.1 Liters etc, up to infinity, in fact between 20 and 21 litres, there is an infinite possibility of outcomes.
Discrete random variables are variables that have a finite possibility of outcomes. the possibilities of occurrences can be counted. For example, if a coin is tossed, the coin can either land on its head or tail, hence there are two possibilities, making the variables discrete
The correct answer is:
It is a continuous random variable (B)
Step-by-step explanation:
Continuous Random Variables are variables that take on a number of possibilities of values that cannot be counted. The values have infinite possibilities. In this example, the height of a Giraffe measured in meters can be an unlimited possibility if values say, 10.5m, 15.22m 12.0m etc. The possibilities are endless.
Discrete Random variables are variables that take on a number of possibility of occurrences that can be counted. For instance, if a dice is rolled, the possibilities can either be a 1, 2, 3, 4, 5 or 6. There are six values that can be gotten, nothing in-between.
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anyone know this answer −4y−4+(−3)
Answer:
− 4 y − 7
Step-by-step explanation:
Remove parentheses.
− 4 y − 4 − 3
Subtract 3 from − 4
− 4 y − 7
.
A 0.01 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are r 0.590, what can you conclude?
Answer:
There is sufficient evidence that there is linear correlation between two variable
Step-by-step explanation:
From the question we are told
The significance level is [tex]\alpha = 0.01[/tex]
The critical value is [tex]a = 0.590[/tex]
The test statistics is [tex]r = 0.591[/tex](linear correlation coefficient )
Now from the data given in the value we see that
[tex]r > a[/tex] so the null hypothesis is rejected
Hence the conclusion is that there is sufficient evidence that there is linear correlation between two variable
Which of the following is the y-intercept of:
2 y = x-8 ?
(0.4)
(-4.0)
(4,0)
(0,4)
PLZ HELP I NEED THE ANSWER QUICK
[tex](0,-4)[/tex] fits the linear equation perfectly.
Hope this helps.
Answer:
the y-intercept is the point (0, -4) on the plane
Step-by-step explanation:
In order to find the y-intercept, write the equation in "slope intercept form" solving for "y":
[tex]2\,y=x-8\\y=\frac{x-8}{2} \\y=\frac{x}{2} -\frac{8}{2} \\y=\frac{x}{2} -4[/tex]
Recall now that the y-intercept is the value at which the line crosses the y-axis (when x = 0), therefore:
[tex]y=\frac{x}{2} -4\\y=\frac{0}{2} -4\\y=-4[/tex]
So the y-intercept is the point (0, -4) on the plane.
Convert 9 days into weeks
Answer:
1 week= 7 days
number of days= 9
number of weeks= 1 week and 2 days
hope it helps :)
please mark it the brainliest!
Answer:
1 week and 2 days
Step-by-step explanation:
Delilah drew 3 points on her paper. When she connects these points,must they form a triangle? Why or why not?
If the three points all fall on the same straight line, then a triangle will not form. Instead, a line will. We call these points to be collinear.
If the points aren't collinear, then a triangle forms.
Answer:
No.
Step-by-step explanation:
The points may be in a straight line, and that doesn't form a triangle.
part 9: I need help. please help me
Answer: A) a² = b² - w² + 2wx
Step-by-step explanation:
b² - (w - x)² = a² - x²
b² - (w² - 2wx + x²) = a² - x²
b² - w² + 2wx - x² = a² - x²
b² - w² + 2wx = a²
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why JOY = LIM
Answer:
Option B
Option E
Step-by-step explanation:
By the use of following postulates we can prove the two right triangles to be congruent.
1). HA - [Equal hypotenuse and an cute angles]
2). LL - [Two legs should be equal]
3). LA - [One leg and one angle must be equal]
4). ASA - [Two angles and the side containing these angles should be equal]
In the given right triangles,
1). OJ ≅ IL
2). ∠O ≅ ∠I
3). ∠J ≅ ∠L
Therefore, two postulates HA, ASA will be applicable for the congruence of the two triangles given.
Options A and E will be the answer.
Answer:
asa, ha, aas
Step-by-step explanation:
10. Which relation is a function?
la A (8, -4), (8, 4), (6, -3), (6, 3).
(0,0)
B (4,7), (8,5), (6,4), (5, 3), (4, 2)
C (0,0), (1, 1), (2, 2), (3, 3), (4,7)
D (0,0), (1,0), (1, 1), (2, 1), (1, 2)
Answer:
C. Why? No repeating x values.
part 8: please assist me with this problem
Answer: d) Neither of the answers are correct
Step-by-step explanation:
Law of Cosines: a² = b² + c² - 2bc · cos A
Note: The letters can be swapped but the letters on the outside must be the same.
Select the fraction with the largest value, 1/5, 1/8, or 3/4
Explain how to identify if the graph of a relation is a function or not
Answer:
[see below]
Step-by-step explanation:
A function is a relation where one domain value is assigned to exactly one range.
An x-value in a function must not repeat.
One way to see if a graph is a function is to use a vertical line test. If the line passes trough the line twice, then it is not a function. On a table, check the x-value column or row. If any of the numbers repeat, then it is not a function. On a mathematical map, check to see if the arrows from a domain number points to one range value on the other side. If it points to two range numbers, then it is not a function.Hope this helps.
if 2/5x+1/x=35 then x=
Answer:
x = 1/25
Step-by-step explanation:
2/5x+1/x=35
[tex]2/5x+1/x=35[/tex]
taking 1/x common
[tex]1/x(2/5+1)=35[/tex]
[tex](2+5)/5=35x\\7/5 = 35x\\x = 7/(5*35) = 1/(5*5) = 1/25[/tex]
Thus, value of x is 1/25
What is the value of 30-2(7+2)-1
Answer: 11
Step-by-step explanation:
30 - 2(7+2)- 1 Distribute or solve parentheses
30 - 14 -4 - 1
30 - 19 = 11
Randomly selected 110 student cars have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars have ages with a mean of 5.3 years and a standard deviation of 3.7 years.
1. Use a 0.02 significance level to test the claim that student cars are older than faculty cars.
Is there sufficient evidence to support the claim that student cars are older than faculty cars?
A. Yes.
B. No.
2. Construct a 98% confidence interval estimate of the difference μ1âμ2, where μ1 is the mean age of student cars and μ is the mean age of faculty cars.
Answer:
1. Yes, there is sufficient evidence to support the claim that student cars are older than faculty cars.
2. The 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].
Step-by-step explanation:
We are given that randomly selected 110 student cars to have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars to have ages with a mean of 5.3 years and a standard deviation of 3.7 years.
Let [tex]\mu_1[/tex] = mean age of student cars.
[tex]\mu_2[/tex] = mean age of faculty cars.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \leq \mu_2[/tex] {means that the student cars are younger than or equal to faculty cars}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1>\mu_2[/tex] {means that the student cars are older than faculty cars}
(1) The test statistics that will be used here is Two-sample t-test statistics because we don't know about the population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)} {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t_n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean age of student cars = 8 years
[tex]\bar X_2[/tex] = sample mean age of faculty cars = 5.3 years
[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years
[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years
[tex]n_1[/tex] = sample of student cars = 110
[tex]n_2[/tex] = sample of faculty cars = 75
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(110-1)\times 3.6^{2}+(75-1)\times 3.7^{2} }{110+75-2} }[/tex] = 3.641
So, the test statistics = [tex]\frac{(8-5.3)-(0)} {3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} } }[/tex] ~ [tex]t_1_8_3[/tex]
= 4.952
The value of t-test statistics is 4.952.
Since the value of our test statistics is more than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we support the claim that student cars are older than faculty cars.
(2) The 98% confidence interval for the difference between the two population means ([tex]\mu_1-\mu_2[/tex]) is given by;
98% C.I. for ([tex]\mu_1-\mu_2[/tex]) = [tex](\bar X_1-\bar X_2) \pm (t_(_\frac{\alpha}{2}_) \times s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} })[/tex]
= [tex](8-5.3) \pm (2.326 \times 3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} })[/tex]
= [tex][2.7 \pm 1.268][/tex]
= [1.432, 3.968]
Here, the critical value of t at a 1% level of significance is 2.326.
Hence, the 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].
It the ratio of boys to girls in 2:5 in the class, how many girls would there be if there are 10 boys?
First set up the ratio 2/5 = 10/x where x is the number of girls.
Now, we can use cross-products to find the missing value.
So we have (2)(x) = (5)(10).
Simplifying, we have 2x = 50.
Dividing both sides by 2, we find that x = 25.
So there are 25 girls in the class if there are 10 boys.
Camera shop stocks six different types of batteries, one of which is type A7b. Suppose that the camera shop has only twelve A7b batteries but at least 30 of each of the other types. Now, answer the following question - How many ways can a total inventory of 30 batteries be distributed among the six different types?
Answer:
The number of ways to distribute 30 batteries among the six different types is 33,649.
Step-by-step explanation:
It is provided that a camera shop stocks six different types of batteries, one of which is type A7b.
Also, the camera shop has only twelve A7b batteries but at least 30 of each of the other types.
Combinations would be used to determine the number of ways to distribute 30 batteries among the six different types. Here repetition is allowed.
[tex]C(n+r-1, r)={n+r-1\choose r}=\frac{(n+r-1)!}{r!(n-1)!}[/tex]
The number of A7b batteries is 12.
Then the number of ways to distribute 30 batteries among the six different types is:
[tex]C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}[/tex]
The number of ways is:
[tex]C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}[/tex]
[tex]=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}\\\\=\frac{(6+(30-12)-1)!}{(30-12)!\times (6-1)!}\\\\=\frac{23!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19\times 18!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19}{ 5!}\\\\=33649[/tex]
Thus, the number of ways to distribute 30 batteries among the six different types is 33,649.
What do you know to be true about the values of a and b?
60"
75"
O A. a b
O B. a = b
O c. a> b
O D. Can't be determined
Answer: B. a = b .
First of all, let's think that a is equal to b.
Then, let's link up these two triangles.
Now, we have a parallelogram.
x+y = a+60
and 75 = b . So, a = b. Then, a is also = 75.
Now apply the basic triangle rule.
75+75+x=180 .. x = 30 degree.
and for the other triangle....
y+75+60=180 .. y= 45 degree...
Now, let's consider that we want to write a as b.
So, x+b+75=180 ...x+b=105
and..
y+b+60=180...y+b = 120..
Then, let's exit the b from these two equations.
-1/ x+b=105
y+b=120
Finally, we found this: y-x =15
and we have already found y and x values.
y was 45 and x was 30 degree.
So when we put these two numbers into that equation y-x=15
we found the value of 15.
So, our answer is a=b.
Answer:
[tex]\huge \boxed{\mathrm{B.} \ a=b}[/tex]
Step-by-step explanation:
The two triangles form a parallelogram.
A parallelogram has opposite angles equal.
75 = b
Adjacent angles in a parallelogram are supplementary to one another.
They add up to 180 degrees.
a + 60 + 75 = 180
a + 135 = 180
Subtract 135 from both sides.
a = 75
Therefore, a = b.
What is the value of x that makes the given equation true? x−3x=2(4+x)
Answer:
x = -2
Step-by-step explanation:
x−3x=2(4+x)
Distribute
x - 3x = 8 +2x
Combine like terms
-2x = 8+2x
Subtract 2x from each side
-2x-2x = 8+2x-2x
-4x = 8
Divide by -4
-4x/-4 = 8/-4
x = -2
Answer:
x-3x=2(4+x)
-2x=8+2x
-2x-2x=8
-4x=8
x=8/-4
x=-2
hope it helps budy x=2
mark me brainliest
what is 3 divided 162
Answer:
0.185185185185185185.........
Step-by-step explanation:
i used a calculator, to the nearst tenth is 0.18 to the nearest 100th is 0.185 also the 185 is repeating so u put a line over the numbers 185
Answer:
3 ÷ 162 = 0.01851851851
If you meant 162 ÷ 3 it is 54
If niether of the two answers above didnt answer your question, then sorry
What's the value of x in the figure? A) 78° B) 57° C) 76° D) 33°
A)78°
135°+a° =180°
a°=45°
57°+x°+a°=180°
57°+x°+45°=180°
102°+x°=180°
x°=180°-102°
x°=78°
the length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58 degree to 36 degree calculate correct to three significant figure the height of the pole
Step-by-step explanation:
(A) Let a triangle be formed with height of pole h, length of base b and angle of elevation 58°. (Due to lack of a figure).
Tan 58° = h / b = 1.6
(B) Let another triangle be formed with height of pole h, length of base (b + 90) and angle of elevation 36°. (Due to lack of a figure).
Tan 36° = h / (b + 90) = 0.72
(C) Simplifying the two equations :
1.6b = 0.72b + 64.8
b = 64.8 / 0.88 = 73.6 m
h (height of pole) = 1.6 * 73.6 = 117.76 m
The distance round a rectangular cafe 35m,the ratio of the length of the cafe to it's width is 3:2 calculate the dimension of the cafe
Hey there! I'm happy to help!
Let's create a basic rectangle with this length to width ratio.
Two sides are 3 and two of them have a length of 2. This would give us a perimeter (distance around) of 10.
We want to find a rectangle with a perimeter of 35 meters with this same ratio. What we can do is multiply all of the dimensions of our first rectangle by 3.5 (to get our perimeter of 10 to 35, we multiply by 3.5).
3×3.5=10.5
2×3.5=7
If we simplify 10.5:7, we have 3:2, and the perimeter of a rectangle with a length of 10.5 and a width of 7 would equal 35 meters.
Have a wonderful day! :D
Point Mis the midpoint of AB. AM = 3x + 3, and AB= 83 – 6.
What is the length of AM?
Enter your answer in the box.
units
Answer:
AM= Half of AB
or, 3x+3=(8x-6)/2
or, 6x+6=8x-6
or, 2x=12
Therefore,x=6
so,AM=3*6+3=21
So the units is 21
Answer:
[tex]\Huge \boxed{21}[/tex]
Step-by-step explanation:
AM = 3x + 3
AB = 8x - 6
Point M is the midpoint of AB.
So, AM = AB/2
3x + 3 = (8x - 6)/2
Multiplying both sides by 2.
2(3x + 3) = 8x - 6
Expanding brackets.
6x + 6 = 8x - 6
Subtracting 6x from both sides.
6 = 2x - 6
Adding 6 to both sides.
12 = 2x
Dividing both sides by 2.
6 = x
Let x = 6 for the length of AM.
3(6) + 3
18 + 3
21
A building company claims that 70% of all new houses they build are finished within 3 weeks. A study show that, over 45 new houses, only 20 have been done in 3 weeks. Does the company claim valid at a level of significance of 0.05 and 0.01
Answer:
Calculated z= 3.515
The Z∝/2 = ±1.96 for ∝= 0.05
The Z∝/2 = ± 2.58 for ∝= 0.01
Yes the company claims valid at a level of significance of 0.05 and 0.01
Step-by-step explanation:
Here p1= 70% = 0.7
p2= 20/45= 0.444 q= 1-p= 1-.444= 0.56
The level of significance is 0.05 and 0.01
The null and alternative hypotheses are
H0; p1= p2 Ha: p1≠p2
The test statistic used here is
Z= p1-p2/ √pq/n
Z= 0.7-0.44/ √ 0.44*0.56/45
z= 0.26/ √0.2464/45
z= 3.515
The Z∝/2 = ±1.96 for ∝= 0.05
The Z∝/2 = ± 2.58 for ∝= 0.01
For the significance level 0.05 reject null hypothesis
For the significance level 0.01 reject null hypothesis
Yes the company claims valid at a level of significance of 0.05 and 0.01
The conjugate of 2+5 i (is) -2 -5 i
True or false
Answer:
False the conjugate of 2+5i is 2-5i .
Step-by-step explanation:
Hope it will help you :)
help please !
m∠1=25°, m∠4=34°, m∠6=146°. Find m∠9
.
Answer:
Option (B)
Step-by-step explanation:
Since all the four rays A, E, D and F are diverging from a point C in the different directions.
Therefore, sum of all the angles formed at a point C will be equal to 360°
m∠1 + m∠4 + m∠6 + m∠9 = 360°
25° + 34° + 146° + m∠9 = 360°
m∠9 = 360° - 205°
= 155°
Therefore, measure of angle 9 is 155°.
Option (B) will be the correct option.
Original population
500
Current population
2,000
Find the percent of increase,
[?]%
Answer: 300%
Step-by-step explanation:
percent of increase: new/old×100%-100%
Since it is percent of increase, you need to subtract the original percent (100%) from the current percent.
------------------
new (current)=2000
old (original)=500
new/old×100%-100%
=2000/500×100%-100%
=4×100%-100%
=400%-100%
=300%
Hope this helps!! :)
Please let me know if you have any question or need further explanation