Answer:
The 2 factors are -2 and 18.
Step-by-step explanation:
xy = -36
Let y = 0.5x - 11 so
x(0.5x - 11) = -36
0.5x^2 - 11x + 36 = 0
0.5(x^2 - 22x + 72) = 0
(x - 4)(x - 18) = 0
x = 4, 18.
Try x = 18:-
The 2 numbers which are factors of -36 must be -2 and 18 because they fit the requirement that 0.5(18) - 11 = 9 - 11 = -2.
A doctor released the results of clinical trials for a vaccine to prevent a particular disease. In these clinical trials, 200,000 children were randomly divided in two groups. The subjects in group 1 (the experimental group) were given the vaccine, while the subjects in group 2 (the control group) were given a placebo. Of the 100,000 children in the experimental group, 21 developed the disease. Of the 100,000 children in the control group, 30 developed the disease.
a) Does it appear to be the case that the vaccine was effective? Use the α = 0.01 level of significance.
Identify the null and alternative hypotheses for this test.
c) Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)
Answer:
1) No, there is not enough evidence to support the claim that the vaccine was effective (P-value=0.104) .
The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
being the subindex 1 for the experimental group and subindex 2 for the control group.
2) Test statistic z=-1.26
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the vaccine was effective.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]
The significance level is 0.01.
The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.
[tex]p_1=X_1/n_1=21/100000=0.0002[/tex]
The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.
[tex]p_2=X_2/n_2=30/100000=0.0003[/tex]
The difference between proportions is (p1-p2)=-0.0001.
[tex]p_d=p_1-p_2=0.0002-0.0003=-0.0001[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=P(z<-1.26)=0.104[/tex]
As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the vaccine was effective.
if georgia has 8 watermelons and ate 2, how many does she have now
Step-by-step explanation:
Now she has 6 watermelons.
Answer:
6 watermelons
Step-by-step explanation:
8-2=6 watermelons
which statement describes the congruent triangles
Answer:
2 triangles
Step-by-step explanation:
2 triangles are said to be congruent when all the corresponding sides of the angle and the interior angles are congruent . The two triangle are said to be the mirror image of each other.
A third grade class has 16 girls and 15 boys a fourth grade class has 18 boys and 15 girls when picking for PE captains will make one selection from the fourth grade class and one selection from the third grade class before the other team pics assuming everyone has an equally like lee chance of being selected what is the probability that the first captain will choose two boys on the first pick
Answer:
[tex]\dfrac{90}{341}[/tex]
Step-by-step explanation:
3rd grade:
Number of girls = 16
Number of boys = 15
Total number of students = 31
4th grade:
Number of girls = 15
Number of boys = 18
Total number of students = 33
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability of picking a boy from 3rd grade, [tex]P_{1} = \dfrac{15}{31} ..... (1)[/tex]
Probability of picking a boy from 4th grade, [tex]P_{2} = \dfrac{18}{33} ..... (2)[/tex]
These are two independent events of picking a boy from 3rd grade and 4th grade.
So, probability the captain chooses 2 boys in the first pick can be found by multiplying (1) and (2) above.
[tex]P = P_{1} \times P_{2}\\\Rightarrow \dfrac{15}{31} \times \dfrac{18}{33}\\\Rightarrow \dfrac{90}{341}[/tex]
Answer:
a
Step-by-step explanation:
What’s the correct answer for this?
Answer:
3 option is correct according to me
Answer:
Second option is the correct answer
[tex](x-2)^{2} =79[/tex]
Step-by-step explanation:
[tex]x^{2} -4x -75=0\\(x^{2} -4x+ 4)-4 -75=0\\(x-2)^{2}-79=0\\(x-2)^{2} =79\implies (x-h)^{2} =p[/tex]
Two towers face each other separated by a distance = 15 m. As seen from the top of the first tower, the angle of depression of the second tower’s base is 60° and that of the top is 30°. What is the height (in meters) of the second tower?
Answer:
Height of second tower = 17.32m
Step-by-step explanation:
I have attached a diagram depicting the question.
From the diagram, The first tower is depicted by side AEB and the second tower CD.
While d is the distance that separates the two towers and it's given as 15m.
Now, since the angle of depression of the second tower’s base is 60°, then for triangle BAC. Angle C = 60°.
Thus; using trigonometric ratios;
tan 60° = AB/AC.
This gives; AB = d*tan 60°
Similarly, for the triangle BED, BE = d*tan 30°
Since, AE = CD, thus ;
CD = AB − BE
CD = d (tan 60° − tan 30°)
CD = 15(1.7321 − 0.5774)
CD = 15 × 1.1547
CD ≈ 17.32 m.
So, height of second tower = 17.32 m
Divide 10x^4-14x³-10x²-10 by x³-3x²+x-2
The quotient is
The remainder is
Answer:
The quotient is [tex]10x+16[/tex]
The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]
Step-by-step explanation:
(See my image for my work)
Once the problem is set up, we need to figure out how to make [tex]x^3[/tex] become [tex]10x^4[/tex]. To do this, we must multiply it by [tex]10x[/tex].
This becomes the first number at the top of our work.
Now, we need to create the second row. To do this, we need to multiply all of the terms on the left by [tex]10x[/tex] and then multiply it by a negative.
Once that is done, we need to subtract these two rows.
After we subtract, we are left with [tex]16x^3-20x^2+26x-10[/tex]
Now we can do the same thing. This time, the number that we must multiply by is 16, so that is the next term on top
Next, we multiply the terms on the left by 16 and then subtract them from the previous expression
This leaves us with [tex]34x^2+10x+22[/tex].
As this has a smaller power than the left-hand side, this is our remainder, which we need to divide by the left hand side.
Our quotient is the number that we have found on the top.
This gives us the answer of
The quotient is [tex]10x+16[/tex]
The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]
(Sorry. This process is hard to do in this form, so I had to write it by hand.)
Answer:
the quotient is 10x + 16
the remainder is 28x² + 10x + 22
4. The ages of the volunteers at a local food
bank are shown below.
3425, 24, 50, 18. 46. 43, 36.32
What is the median of this set of data?
A 32
0 34
331
(D) 50
Answer:
The median is 43
Step-by-step explanation:
I dont know why your answers dont have any of them,cause with the numbers
3425, 24, 50, 18. 46. 43, 36.32
that makes your median is 43
a cruise ship has a large , circular window. It has a diameter of 6 meters. What is the windows area?
Answer:
28.26
hop thats better the the first anser
Solve 9x2 + 6 = 12x
Answer:
9x^2 - 12x + 6 =0
work is pictured and shown
12 is 1/3 of what number
Answer:
The number is 36.
Step-by-step explanation:
Given that 1/3 of a number is 12. So let's make this number into any variable, I will choose x which means that 1/3 of x is equals to 12. Next we have to write an expression :
[tex] \frac{1}{3} \times x = 12[/tex]
In order to solve x, you have to multiply 3 to both sides :
[tex] \frac{1}{3} \times x \times 3 = 12 \times 6[/tex]
[tex]x = 36[/tex]
To find out what number 12 is one-third of, we can set up an equation. Let's assume the unknown number is represented by "x".
According to the given statement, we can write the equation as: 12 = (1/3)x To solve for x, we need to isolate it on one side of the equation.
We can do this by multiplying both sides of the equation by 3, canceling out the fraction: 3 * 12 = (1/3)x * 3 36 = x Therefore, 12 is one-third of 36. In other words, if we take one-third of 36, it will equal 12.
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Find he least common multiple of 16, 21, and 24
Answer:
336 is the answer
Step-by-step explanation:
hope this helps
What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
The centre coordinates would be the opposite value of what is in the brackets
For example, the x value in the brackets is -3, the centre coordinate x value would be positive 3
The same would apply to the y value
The radius would be the square root of 36
Thus, your answer would be option A
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Stay Brainly! ヅ
- Ally ✧
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A researcher wanted to test the claim that, "Seat belts are effective in reducing fatalities." A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. If a significance level of 5% is used, which of the following statements gives the correct conclusion?
a. Since p >α we conclude that this data shows that seat belts are effective in reducing fatalities.
b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities U
c. Since p >α we conclude that this data shows that seat belts aren't effective in reducing fatalities.
d. Since p<α, we conclude that this data shes that seat belts aren't effective in reducing fatalities.
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the occupants not wearing seat belts and occupants wearing seat belts. The population proportion of occupants not wearing seat belts and occupants wearing seat belts would be p1 and p2 respectively.
P1 - P2 = difference in the proportion of occupants not wearing seat belts and occupants wearing seat belts.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 > p2
p1 - p2 > 0
it is a right tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples.
For occupants not wearing seat belts,
x1 = 31
n1 = 2823
P1 = 31/2823 = 0.011
For occupants wearing seat belts,
x2 = 16
n2 = 7765
P2 = 16/7765 = 0.0021
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (31 + 16)/(2823 + 7765) = 0.0044
1 - pc = 1 - 0.0044 = 0.9956
z = (P1 - P2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.011 - 0.0021)/√(0.0044)(0.9956)(1/2823 + 1/7765) = - 0.0089/0.00145462023
z = 6.81
From the normal distribution table,
p < 0.00001
0.00001 < 0.05, we would reject the null hypothesis.
Therefore,
b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities
What is the arc length if the radius is 12 cm?*
A
B
60°
O 12 pi cm
O 3 pi cm
O 4 pi cm
024 pi cm
Answer:
4π cm
Step-by-step explanation:
The length of an arc of a circle with radius r and central angle θ is given by ...
s = rθ
where θ is in radians.
Here, your arc measures 60° = π/3 radians, so the arc length is ...
s = (12 cm)(π/3) = 4π cm
») What kind of triangle is this?
9
17
16
Answer:
scalene
Step-by-step explanation:
We know it isn't a right triangle because it doesn't satisfy the Pythagorean Theorem (9² + 16² ≠ 17²). Because the lengths of the sides are all different, it can't be an equilateral (all equal sides) or an isosceles (2 equal sides) either. Therefore, it is a scalene triangle (all 3 sides different). Hope this helps!
HELP PLEASE
The table shows Amy's, Jenny's, and Meg's sales for the month of February. They get a 5% commission on their sales. Which matrix gives the commission they earned for each type of product?
Answer:
a
Step-by-step explanation:
A percentage is a way to describe a part of a whole. The correct matrix is C.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that the table shows Amy's, Jenny's, and Meg's sales for the month of February. They get a 5% commission on their sales. Therefore, the commission on each product category and for each person can be calculated as shown below.
Commission on book sales for Amy, a₁₁ = 120 × 0.05 = 6
Commission on book sales for Jenny, a₁₂= 250× 0.05 = 12.5
Commission on book sales for Meg, a₁₃ = 215 × 0.05 = 10.75
Commission on Games sales for Amy, a₂₁ = 155 × 0.05 = 7.75
Commission on Games sales for Jenny, a₂₂= 106 × 0.05 = 5.3
Commission on Games sales for Meg, a₂₃ = 175 × 0.05 = 8.75
Commission on Tables sales for Amy, a₃₁ = 350 × 0.05 = 17.5
Commission on Tables sales for Jenny, a₃₂= 400 × 0.05 = 20
Commission on Tables sales for Meg, a₃₃ = 290 × 0.05 = 14.5
Now, the matrix can be made as shown below,
[tex]\left[\begin{array}{ccc}6&12.5&10.75\\7.75&5.3&8.75\\17.5&20&14.5\end{array}\right][/tex]
Hence, the correct matrix is C.
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A 2-kilogram bag of sugar costs $5.09. What is the unit price, rounded to the nearest cent?
Answer:
$2.55 per kilogram bag of sugar.
Step-by-step explanation:
To calculate the cost of only 1 bag of sugar, you would take what you know - 2 kilograms costs $5.09 - and use that to determine your answer.
Since you know how much 2 bags costs, and you need to know the cost of 1, you would divide the cost of 2 bags of sugar by 2. (5.09 ÷ 2)
That equals 2.545, but since the problem is asking you to round to the nearest cent, you would end up with -------> $2.55
Hope this helps!
stay safe
The owner of a 5000-gal oil truck loads the truck with gasoline and kerosene. The profit on each gallon of gasoline is 16¢ and on each gallon of kerosene it is 15¢. How many gallons of each fuel did the owner load if the profit was $780?
Answer:
3000 gallons of gasoline and 2000 gallons of kerosene
Step-by-step explanation:
The first thing is that 16 ¢ and 15 ¢ are 16 and 15 cents, therefore we can express it as $ 0.16 and $ 0.15 respectively.
Now, we can solve by means of a 2x2 system of equations, we have to:
"x" is the number of gallons of gasoline
"y" be the number of gallons of kerosene
x + y = 5000 => x = 5000 - y
0.16 * x + 0.15 * y = 780
replacing
0.16 * (5000 - y) + 0.15 * y = 780
800 - 0.16 * y + 0.15 * y = 780
-0.01 * y = 780 - 800
y = -20 / -0.01
y = 2000
Therefore x:
x = 5000 - 2000
x = 3000
which means 3000 gallons of gasoline and 2000 gallons of kerosene
In 25 years, a bond with a 4.75% annual interest rate earned $2,375 as interest. What was the principal amount of the bond?
Answer:
Denote the principal amount: P
In 25 years, a bond with a 4.75% annual interest rate earned $2,375 as interest.
=> P x (1 + 4.75/100)^25 - P = 2375
=> P x 3.19 - P = 2375
=> P x 2.19 = 2375
=> P = 2375/2.19 = 1084.48$
Hope this helps!
:)
Answer:$2000
Step-by-step explanation:
Someone please help me with this! Is this a independent or dependent? Explain why.
Answer:
independent
Step-by-step explanation:
Dependent equations graph as the same line. These lines are not the same, so the equations are independent.
___
However, the lines are parallel, so the equations are also inconsistent. There is no solution to this system of equations.
Which shows one way to determine the factors of x3 + 11x2 – 3x – 33 by grouping?
Step-by-step explanation:
One way
x3 + 11x2 - 3x - 33
x2(x + 11) - 3(x + 11)
(x + 11) (x2 - 3) are the factors
Which statement best describes the polynomial?
-24x7 – 12x2 - 9x+6
Answer:
a. It is in standard form because the exponents are in order from highest to lowest.
Complete question:
a. It is in standard form because the exponents are in order from highest to lowest.
b. It is in standard form because the coefficients are in order from highest to lowest.
c. It is not in standard form because the constant should be the first term.
d. It is not in standard form because it can be further simplified.
Step-by-step explanation:
-24x^7-12x^2-9x+6
A polynomial is in standard form when the exponents are in order from highest to lowest. In the given expression , the exponent is in order x^7 and then x^2 and then x and constant.
Standard form does not depends on the coefficient of each each.
The given polynomial is in standard form because the exponent are in order from highest to lowest.
Answer:
A
Step-by-step explanation:
What are the first three terms of the sequence modeled by the recursive function An=1/2a n-1 , when a1=1?
Answer:
A on edge trust
Step-by-step explanation:
The first three term of the sequence are,
⇒ 1/2 , 1/4, 1/8
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The recursive function is,
⇒ [tex]A_{n} = \frac{1}{2} a_{n - 1}[/tex]
And, We have;
⇒ a₁ = 1
Now, The recursive function is,
⇒ [tex]A_{n} = \frac{1}{2} a_{n - 1}[/tex]
Put n = 2;
⇒ [tex]A_{2} = \frac{1}{2} a_{2 - 1}[/tex]
⇒ [tex]A_{2} = \frac{1}{2} a_{1}[/tex]
⇒ [tex]A_{2} = \frac{1}{2}\ * 1[/tex]
⇒ [tex]A_{2} = \frac{1}{2}[/tex]
Put n = 3;
⇒ [tex]A_{3} = \frac{1}{2} a_{3 - 1}[/tex]
⇒ [tex]A_{3} = \frac{1}{2} a_{2}[/tex]
⇒ [tex]A_{3} = \frac{1}{2}\ * \frac{1}{2}[/tex]
⇒ [tex]A_{3} = \frac{1}{4}[/tex]
Put n = 4;
⇒ [tex]A_{4} = \frac{1}{2} a_{4 - 1}\\[/tex]
⇒ [tex]A_{4} = \frac{1}{2} a_{3}[/tex]
⇒ [tex]A_{4} = \frac{1}{2}\ * \frac{1}{4}[/tex]
⇒ [tex]A_{4} = \frac{1}{8}[/tex]
Thus, The first three term of the sequence are,
⇒ 1/2 , 1/4, 1/8
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v=1/6√π S 3/2 find V when s=60m'2 π=3.14
Answer:
137.26 m^3
Step-by-step explanation:
Put the numbers into the formula and do the arithmetic.
v = (1/6)(√3.14)(60 m^2)^(3/2) = 137.26 m^3
What’s the correct answer for this?
Answer:
(0,2)
Step-by-step explanation:
2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB
Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0
Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2
The point is (0,2)
which number is located between 1.2 and 1.4
Answer: 1.3
Step-by-step explanation: Ok, let's make a number line...
0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6
From the number line, the only number that fits is 1.3
I hope this helps!
Answer:
1.3
Step-by-step explanation:
Hope this helps have a wonderful day
The original price, p, of a pair of shoes was discounted by 20% and a sales tax of 8% was applied to the sales price. Which expression is equivalent to the new price?
Answer:
0.864p
Step-by-step explanation:
A discount of 20% is (1 - .2) = .8
8% tax is 1.08
.8 * 1.08 = 0.864
That means the new price is 0.864p
Kenney High School's swimming pool is 25 yards long. The pool has 8 lanes, each of which is 3 yards wide. The pool is filled to a depth of 6 feet.
What are the lengths and width in terms of feet?
Answer:
length: 75 ftwidth: 72 ftStep-by-step explanation:
Length: (25 yd)(3 ft/yd) = 75 ft.
Width: (8 lanes)(3 yd/lane)(3 ft/yd) = 72 ft.
The length and width are 75 ft and 72 ft, respectively.
Answer:
length; 75 ft
width; 72 ft
Step-by-step explanation:
Choose the correct simplification of the expression (4x3y2z4)(2x3y4z3)
Answer:
[tex]=8x^6y^6z^7[/tex]
Step-by-step explanation:
[tex](4x^3*y^2*z^4)(2x^3*y^4*z^3)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\\:a^c=a^{b+c}\\=4y^2z^4\cdot \:2x^{3+3}y^4z^3\\\mathrm{Add\:the\:numbers:}\:3+3=6\\=4y^2z^4\cdot \:2x^6y^4z^3\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\y^2y^4=\:y^{2+4}\\=4z^4\cdot \:2x^6y^{2+4}z^3[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\z^4z^3=\:z^{4+3}\\=4\cdot \:2x^6y^6z^{4+3}\\\mathrm{Add\:the\:numbers:}\:4+3=7\\=4\cdot \:2x^6y^6z^7\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2=8\\=8x^6y^6z^7[/tex]