Answer:
d) The t-distribution with 5 degrees of freedom must be used
Step-by-step explanation:
For cases of Normal Distribution where the variance is unknown and the sample size n is smaller than 30, we must use the t-student distribution.
The shape of the curve for t-student is bell-shape (flatter and with wider tails than the bell shape of normal distribution.
Actually, when we deal with t-student distribution we are dealing with a family of curves that will become closer and closer to the bell shape of the normal distribution as the degree of freedom increases. From values of n =30( and bigger), we can assume that the curve of t-student is the same as for normal distribution
Raven has a bag of 33 red and black marbles. The number of red marbles is 6 more than double the number of black marbles. Let r represent the number of red marbles and b represent the number of black marbles. Which statements about the marbles are true? Check all that apply. The equation r + b = 33 represents the total number of marbles. The equation r = 2 b + 6 can be used to find the number of red marbles. The equation r = 2 b + 6 represents the total number of marbles. The equation r + b = 33 can be used to find the number of red marbles. There are 9 red marbles in the bag. There are 9 black marbles in the bag. There are 24 black marbles in the bag. There are 24 red marbles in the bag.
Hey there! I'm happy to help!
If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.
r=2b+6
We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.
2b+6+b=33
We combine like terms.
3b+6=33
We subtract six from both sides.
3b=27
We divide both sides by 3.
b=9
Now we just subtract 9 from 33 to see how many red ones there are.
33-9=24
So, there are 24 red marbles and 9 black marbles.
Now, let's see which of these options are correct.
The equation r+b=33 represents the total number of marbles.
This is true because r plus b is equal to the total, which is 33.
The equation r=2b+6 can be used to find the number of red marbles.
This is true because it we used this r-value to find how many black marbles there were.
The equation r=2b+6 represents the total number of marbles.
This is false because it does not have the total number, which is 33.
The equation r=b=33 can be used to find the number of red marbles.
This is true because we plugged in the r-value to solve for b with this equation.
There are 9 red marbles in the bag.
This is false. There are 24 red marbles.
There are 9 black marbles in the bag.
This is true.
There are 24 black marbles in the bag.
This is false. There are 9 black marbles.
There are 24 red marbles in the bag.
This is true.
Have a wonderful day! :D
Answer:
1,2,4,6,8
Step-by-step explanation:
Suppose that MNO is isosceles with base NM. Suppose also that =m∠N+4x7° and =m∠M+2x29°. Find the degree measure of each angle in the triangle.
Answer:
m∠N = 51°
m∠M = 31°
m∠O = 98°
Step-by-step explanation:
It is given that ΔMNO is an isosceles triangle with base NM.
m∠N = (4x + 7)° and m∠M = (2x + 29)°
By the property of an isosceles triangle,
Two legs of an isosceles triangle are equal in measure.
ON ≅ OM
And angles opposite to these equal sides measure the same.
m∠N = m∠M
(4x + 7) = (2x + 29)
4x - 2x = 29 - 7
2x = 22
x = 11
m∠N = (4x + 7)° = 51°
m∠M = (2x + 9)° = 31°
m∠O = 180° - (m∠N + m∠M)
= 180° - (51° + 31°)
= 180° - 82°
= 98°
A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? No replacement. Round to four decimal places.
Answer:
0.2006
Step-by-step explanation:
The probability the first calculator is defective is 42/62.
The probability the second calculator is defective is 41/61.
The probability the third calculator is defective is 40/60.
The probability the fourth calculator is defective is 39/59.
The probability all four calculators are defective:
(42/62) (41/61) (40/60) (39/59) = 0.2006
a truck and a car drive uniformly among the expressway from city a to city b. The truck leaves at 09:15 am and arrives at 1:15 pm. The car leaves at 10:00 am and arrives at 12:45 pm. At what times does the car overtake the truck? please help
Answer:
the car overtake the truck at time 11:40 am.
Step-by-step explanation:
We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.
We will express the time in hours (and decimals of hours).
The truck speed can be calculated estimating the time between arrival and start:
- The arrival time is 1.15 pm. This is t2=13.25.
- The starting time is 9:15 am. This is t1=9.25.
The truck took t2-t1=13.25-9.25=4 to go from city a to b.
The average speed is then:
[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]
We can write the equation for the position x(t) for the truck as:
[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]
For the car we have:
- The arrival time is 12:45 am. This is t2=12.75.
- The starting time is 10 am. This is t1=10.
The car took t2-t1=12.75-10=2.75.
The average speed is then:
[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]
We can write the equation for the position x(t) for the car as:
[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]
The time at which the car overtake the car is the time when both vehicles have the same position:
[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]
The car overtakes the truck at t=11.65 hours or 11:39 am.
3
Easton mixed
kg of flour with
kg of sugar.
6
Determine a reasonable estimate for the amount of flour and sugar combined.
Choose 1 answer:
1
Less than
2
kg
B
More than
1
kg but less than 1 kg
2
More than 1 kg
A bag contains six balls labeled 1 through 6. One ball will be randomly picked.
What is the probability of picking an odd number?
Write your answer as a fraction in simplest form.
S = sample space = set of all possible outcomes
S = set of whole numbers 1 through 6
S = {1,2,3,4,5,6}
E = event space = set of outcomes we want to happen
E = set of odd numbers between 1 through 6
E = {1,3,5}
We have 3 items in set E and 6 items in set S. So there are 3 ways to get what we want to happen out of 6 ways total. The probability is therefore 3/6 = 1/2
Answer: 1/2A sign company is creating a pennant in the shape of an equilateral triangle
The length of each side is 8 inches. What is the alttitude length so the
company will know what size box to ship the pennant in?
Hey there! :)
Answer:
4√3 in.
Step-by-step explanation:
Given:
-Equilateral triangle
-Side lengths of 8 in
Find the altitude using the Pythagorean Theorem (c² = a² + b²) where:
'a' is the shorter leg, or half of the base to find the altitude
'b' is the altitude
'c' is the Hypotenuse, or 8 in.
Therefore:
8² = 4² + b²
64 = 16 + b²
48 = b²
b = √48 or 4√3 in.
Therefore, the altitude of the triangle is 4√3 in.
A system of equations is shown below: Equation A: 3c = d − 8 Equation B: c = 4d + 8 Which of the following steps should be performed to eliminate variable d first?
Answer:
multiplying the equation A
Step-by-step explanation:
3c=d-8 ####### *4
+ c=4d + 8
After that you will get the value of c and d.
Answer:
Multiply equation A by -4
Step-by-step explanation:
3c = d - 8
c = 4d + 8
Multiply equation A by -4.
-12c = -4d + 32
c = 4d + 8
Add the equations.
-11c = 40
Variable d is eliminated.
Hong buys a bag of 11 tangerines for $2.86.
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Answer:
$0.26
Step-by-step explanation:
To find the unit price, divide the cost by the amount you have.
$2.86/11 = $0.26
The unit price is $0.26.
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
Suppose you are climbing a hill whose shape is given by the equation z = 1600 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1464). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend?
Answer:
you will start to ascend at the rate of 1.6
Step-by-step explanation:
Walking south, it's the negative part of a coordinate, so the unit vector at this point is; u = (0,-1)
We are told that the equation z = 1600 − 0.005x² − 0.01y²
Therefore, we have;
∇z = ((δ/δx)i + (δ/δx)j)(1600 − 0.005x² − 0.01y²)
This gives;
∇z = -0.005(2x)i - 0.01(2y)j
∇z = <-0.01x - 0.02y>
coordinates are (120, 80, 1464).
Thus;
∇z(120, 80, 1464) = <-0.01(120), - 0.02(80)> = <-1.20, -1.60>
D_uf = <-1.20, -1.60> × <0, - 1>
D_uf = 0 + 1.6
D_uf = 1.6
So, you will start to ascend at the rate of 1.6
Determine whether the function below is an even function, an odd function, both, or neither.
f(x)=x^6 + 10x^4-11x^2+19
ОА.
neither even nor odd
OB.
odd function
Ос.
both even and odd
OD.
even function
Reset
Next
Answer:
Step-by-step explanation:
even function are symmetrical about the y axis or f(-x)=f(x)
odd function are symmetrical about the origin -f(-x)=f(x)
f(x)=x^6 + 10x^4-11x^2+19
f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19
the function is even
Suppose a city official conducts a hypothesis test to test the claim that the majority of voters oppose a proposed school tax. Assume that all of the conditions fro proceeding with a one-sample test on proportions have been met. The calculated test statistic is approximately 1.23 with an associated p-value of approximately 0.1093. Choose the conclusion that provides the best interpretation for the p-value at a significance level of alpha = 0.05.
A. If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is surprising (or considered unusual) and could not easily happen by chance.
B. If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance
C. The p-value should be considered extreme: therefore, the hypothesis test proves that the null hypothesis is true
D. none of the above
Answer:
The correct option is (B).
Step-by-step explanation:
The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.
In this case, we need to test the claim that the majority of voters oppose a proposed school tax.
The hypothesis can be defined as follows:
H₀: The proportion of voters opposing a proposed school tax is not a majority, i.e. p ≤ 0.50.
Hₐ: The proportion of voters opposing a proposed school tax is a majority, i.e. p > 0.50.
It is provided that the test statistic value and p-value are:
z = 1.23
p-value = 0.1093
The probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic is 0.1093.
The significance level of the test is:
α = 0.05
The p-value of the test is larger than the significance level of the test.
p-value = 0.1093 > α = 0.05
The null hypothesis will not be rejected.
Concluding that there is not enough evidence to support the claim.
Thus, the correct option is:
"If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance"
What percentage of babies born in the United States are classified as having a low birthweight (<2500g)? explain how you got your answer?
Answer:
2.28% of babies born in the United States having a low birth weight.
Step-by-step explanation:
The complete question is: In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.
We are given that in the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.
Let X = birth weights of newborn babies
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 3,500 g
[tex]\sigma[/tex] = standard deviation = 500 g
So, X ~ N([tex]\mu=3500, \sigma^{2} = 500[/tex])
Now, the percent of babies born in the United States having a low birth weight is given by = P(X < 2500 mg)
P(X < 2500 mg) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{2500-3500}{500}[/tex] ) = P(Z < -2) = 1 - P(Z [tex]\leq[/tex] 2)
= 1 - 0.97725 = 0.02275 or 2.28%
The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.
Answer:
The z-score for 2,500 is -2. According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g. 5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g. Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500 g.
Step-by-step explanation:
did the assignment on edge:)
A special tool manufacturer has 50 customer orders to fulfill. Each order requires one special part that is purchased from a supplier. However, typically there are 2% defective parts. The components can be assumed to be independent. If the manufacturer stocks 52 parts, what is the probability that all orders can be filled without reordering parts
Answer:
0.65463
Step-by-step explanation:
From the given question:
It is stated that 2% of the parts are defective (D) out of 50 parts
Therefore the probability of the defectives;
i.e p(defectives) = [tex]\dfrac{N(D)}{N(S)}[/tex]
p(defectives) = [tex]\dfrac{2}{50}[/tex]
p(defectives) = 0.04
The probability of the failure is the P(Non-defectives)
p(Non-defectives) = 1 - P(defectives)
p(Non-defectives) = 1 - 0.04
p(Non-defectives) = 0.96
Also , Let Y be the number of non -defective out of the 52 stock parts.
and we need Y ≥ 50
P( Y ≥ 50) , n = 52 , p = 0.96
P( Y ≥ 50) = P(50 ≤ Y ≤ 52) = P(Y = 50, 51, 52)
= P(Y = 50) + P(Y =51) + P(Y=52) (disjoint events)
P(Y = 50) = [tex](^{52}_{50}) ( 0.96)^{50}(1-0.96)^2[/tex]
[tex]P(Y = 50) = 1326 (0.96)^{50}(0.04)^2[/tex]
P(Y = 50) = 0.27557
P(Y = 51) =[tex](^{52}_{51}) ( 0.96)^{51}(1-0.96)^1[/tex]
[tex]P(Y = 51) = 52(0.96)^{51}(0.04)^1[/tex]
P(Y = 51) = 0.25936
(Y = 52) =[tex](^{52}_{52}) ( 0.96)^{52}(1-0.96)^0[/tex]
[tex]P(Y = 52) = 1*(0.96)^{52}(0.04)^0[/tex]
P(Y = 52) = 0.1197
∴
P(Y = 50) + P(Y =51) + P(Y=52) = 0.27557 + 0.25936 + 0.1197
P(Y = 50) + P(Y =51) + P(Y=52) = 0.65463
A line passes through the points ( – 4, – 2) and ( - 1, - 2). Determine the slope of the line.
Answer: -4/3
Step-by-step explanation:
Formula to find a slope of two given points is
y(sub2) - y(sub1) / x(sub2) - x(sub1)
Plug the values in to get the answer.
-2 - 2 / -1 - (-4)
-4/3
what is improper sampling in statistical analysis and how can i use it in day-to-day life
Answer:
Statistical concepts are used in quality testing. Companies make many products on a daily basis and every company should make sure that they sold the best quality items.
Step-by-step explanation:
pls keep brainly questions only school related thank you!
Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: , , , , , . Use a significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?
Answer: There is no sufficient evidence to support the claim that loaded die behaves differently than a fair die
Step-by-step explanation:
Find explanations in the attached file
A firm has the marginal-demand function Upper D prime (x )equalsStartFraction negative 1200 x Over StartRoot 25 minus x squared EndRoot EndFraction . Find the demand function given that Dequals16 comma 000 when x equals $ 4 per unit.
Answer:
The demand function is [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]
Step-by-step explanation:
A firm has the marginal-demand function [tex]D' x = \dfrac{-1200}{\sqrt{25-x^2 } }[/tex].
Find the demand function given that D = 16,000 when x = $4 per unit.
What we are required to do is to find the demand function D(x);
If we integrate D'(x) with respect to x ; we have :
[tex]\int\limits \ D'(x) \, dx = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
Let represent t with [tex]\sqrt{25-x^2}}[/tex]
The differential of t with respect to x is :
[tex]\dfrac{dt}{dx}= \dfrac{1}{2 \sqrt{25-x^2}}}(-2x)[/tex]
[tex]\dfrac{dt}{dx}= \dfrac{-x}{ \sqrt{25-x^2}}}[/tex]
[tex]{dt}= \dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]
replacing the value of [tex]\dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex] for dt in [tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
So; we can say :
[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]
[tex]D(x) = 1200\int\limits{\dfrac{- x}{\sqrt{25-x^2}} } \, dx[/tex]
[tex]D(x) = 1200\int\limits \ dt[/tex]
[tex]D(x) = 1200t+ C[/tex]
Let's Recall that :
t = [tex]\sqrt{25-x^2}}[/tex]
Now;
[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex]
GIven that:
D = 16,000 when x = $4 per unit.
i.e
D(4) = 16000
SO;
[tex]D(x) = 1200(\sqrt{25-x^2}})+ C[/tex]
[tex]D(4) = 1200(\sqrt{25-4^2}})+ C[/tex]
[tex]D(4) = 1200(\sqrt{25-16}})+ C[/tex]
[tex]D(4) = 1200(\sqrt{9}})+ C[/tex]
[tex]D(4) = 1200(3}})+ C[/tex]
16000 = 1200 (3) + C
16000 = 3600 + C
16000 - 3600 = C
C = 12400
replacing the value of C = 12400 into [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex], we have:
[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]
∴ The demand function is [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]
Find the measure of y. Polygon Angle-Sum theorems
Answer:
z = 70°
y = 103°
Step-by-step explanation:
From the picture attached,
110° + z° = 180° [Supplementary angles]
z = 180 - 110
z = 70°
Since sum of interior angles of a polygon = (n - 2)×180°
where n = number of sides of the polygon
For a quadrilateral (n = 4),
Sum of interior angles = (4 - 2) × 180°
= 360°
z° + y° + 100° + 87° = 360°
70° + y° + 187° = 360°
y = 103°
Therefore, measure of the angles x = 70° and y = 103°.
plzZZZZZZzzzzzzzzzZZZZZzzzzzzzZZZzzzzzZZzzzzZZzzzzZzz help for my friend thank you
Answer:
Likely
Step-by-step explanation: Mathematically it is likely because there are 4 options certain is the thing that will defiantly happen so it would be 4/4. The impossible thing would be 1/4 this is because 1/4 is the smallest so it is obviously going to be impossible. Likely would be 3/4 and unlikely would clearly be 2/4
Answer:
it is likely
Step-by-step explanation:
it is not certant because it is not 4/4 but it is not impossible because its not 0/4 so the answer is likely 3/4
NEED URGENT HELP ON 5 QUESTIONS SIMILAR TO THIS!!!!! WILL GIBE BRAINLIEST AND 5 STARS IF CORRECT QUICKLY! - 50 POINT - also, no wrong answers just for the points please.
Answer:
As X → - ∞ , y → ∞ and as x→ ∞ , y → ∞
option c is the correct option.Step-by-step explanation:
let f(x) = y = 3x² - 5x + 2
y = 3x² - 5x + 2
= x ( 3x - 5 ) + 2
y = ∞ ( 3 ( ∞ - 5 ) ) + 2
= ∞ (∞ ) + 2
y = ∞
y → ∞ as x → ∞
Now,
as x → - ∞
y = x ( 3x - 5 ) + 2
= ∞ ( 3 ( - ∞ ) - 5 ) + 2
= - ∞ ( - ∞ ) + 2
∞² + 2 = ∞
Hence , Option C is the correct answer.
Answer:
Mathematically you can use the following V = ⁴⁄₃πr³
π = pi
r = radius
To do this you would need a set of scales, a jug, some water, a pen, a ruler and some paper.
ωα√
Zen spent $255 on a bag and a belt. She wanted to buy another
similar bag with the remaining money but was short of $30. In the
end, she bought another similar belt and had $15 left in the end.
(a) How much more did the bag cost than the belt?
(b) How much did the belt cost?
Answer:
A)$ 45
B) $105
Step-by-step explanation:
Bag and a belt cost $255
Let bag = x
Let belt = y
X+y= 255 equation 1
Let total money be z first
Remaining money= z-255
X-30 = z-255
Y +15 = z-255
Equating the left side of the equation
X+30 = y+15
X-y= 45 equation 2
Solving simultaneously
X+y= 255
X-y= 45
2x = 300
X= 150
If x= 150
150-y= 45
150-45= y
105=y
Bag = $150
Belt = $105
Bag Is 150-105 more than the belt
150-105= $45
18. Which of the following equations is equivalent to 25x = 7?
A. x=
log2 (3)
+1+9= 3? Is
B.
log27
5
C.
X=
log, 2
5
log, 5
D. x=
2
Answer:
x = log (7)/ 2log 5
Step-by-step explanation:
25^ x = 7
Replace 25 with 5^2
5^ 2x = 7
Take log on each side
log (5 ^2x) = log ( 7)
We know that log a^ b = b log a
2x log 5 = log (7)
Divide each side by log 5
2x log 5/ log 5= log (7)/ log 5
2x = log (7)/ log 5
Divide each side by 2
x = log (7)/ 2log 5
FOR BRAINLIEST ANSWER HURRY HELP THANKS If (a,b) is a point in quadrant IV, what must be true about a? What must be true about b?
Answer:
Well if (a,b) is in Quadrant IV which is the last quadrant the a or x is a positive number and the b or y is a negative number.
Answer:
a should be a positive number
b should be a negative number
Chapter Reference
b
A board 65 inches long is sawed into two pieces, so that one piece is 7 inches shorter than twice the length of the other piece ? Find the length of the two pieces .
Step-by-step explanation:
It is given that,
Total length of a board is 65 inches
It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.
Let x is the length of other piece and y is the length of first piece such that,
y = 2x-7 ....(1)
Also,
x+y = 65 .....(2)
Put the value of y from equation (1) to equation (2) such that,
x+2x-7 = 65
3x=65+7
3x=72
x = 24 inches
Put the value of x in equation (1)
y = 2(24)-7
y = 41 inches
So, the length of first piece is 41 inches while the length of other piece is 24 inches.
please help!! shirley is drawing triangle that have the same area
Answer:
12 and 7
Step-by-step explanation:
The area of the first triangle is
A = 1/2 bh
A = 1/2 ( 14*6)
A = 42
The area of the second triangle must equal 42
Varying inversely means as the height increases, the base must decrease at the same rate
Lets try 12 and 7
A = 1/2 (12*7)
A = 42
The height of the new triangle increased and the base decreased
Answer:
[tex]\boxed{12 \: \mathrm{and} \: 7}[/tex]
Step-by-step explanation:
Solve for the area of first triangle.
[tex]\frac{bh}{2}[/tex]
[tex]b=base\\h=height[/tex]
[tex]\frac{14 \times 6}{2}[/tex]
[tex]\frac{84}{2} =42[/tex]
The area of second triangle is same as the first triangle.
The area of second triangle is 42 units².
The base varies inversely with the height.
[tex]b \propto \frac{1}{h}[/tex]
As the value of b increases, the value of h decreases.
[tex]\frac{12 \times 7}{2}=42[/tex]
The answer is b = 12 and h = 7.
solve for the inequality ᵏ⁄₄ ≥ 6
Answer:
k ≥ 24
Step-by-step explanation:
ᵏ⁄₄ ≥ 6
Multiply each side by 4
ᵏ⁄₄ *4 ≥ 6*4
k ≥ 24
Answer:
k≥24
Step-by-step explanation:
k/4≥6
Use the multiplication property of equality by multiplying both sides by 4 to get
k≥24
If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem
Thank you
If the sample size is nequals9, what is the standard deviation of the population from which the sample was drawn?
Answer:
13.33
Step-by-step explanation:
As in the attached diagram, we can see that the points belong to [tex]\mu\pm \sigma[/tex] interval
Data provided in the question as per the details below:
[tex]\mu_{\bar x}[/tex] = 440
[tex]\mu_{\bar x} + \sigma_{\bar x}[/tex] = 480
So,
[tex]\sigma_{\bar x}[/tex] = 480 - 440
= 40
Now the standard deviation of the population is
[tex]V(\bar{x}) = \frac{\sigma}{\sqrt n} \\\\ = \frac{40}{\sqrt 9}[/tex]
= 13.33
Hence, the standard deviation of the population for which the sample is drawn is 13.33
Select a committee of 3 people from your staff of 9. How many different ways can this be accomplished when one person will be the lead, one will be the record keeper, and one will be the researcher
Answer:
504 ways.
Step-by-step explanation:
In this case, order matters. If Amy were lead, Bob were record keeper, and Charles were researcher, that would be different than if Bob were lead, Charles were record keeper, and Amy were researcher. So, we will be using a permutation formula to compute.
The formula is n! / (n - k)!, where n is the total number of people (9), and k is the number you are selecting (3).
9! / (9 - 3)! = 9! / 6! = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1) = 9 * 8 * 7 = 72 * 7 = 504 ways.
Hope this helps!