Answer:
d≤7
Step-by-step explanation:
-10d≥-70
d≤7
It has been estimated that as many as 70% of the fish caught in certain areas of the Great Lakes have liver cancer due to the pollutants present. Find an approximate 95% range for the percentage of fish with liver cancer present in a sample of 130 fish.
Answer:
62.12% to 77.88%
Step-by-step explanation:
We proceed as follows mathematically;
From the question
n=130
Estimate for sample proportion=70% = 70/100 = 0.7 = p
Level of significance is =1-0.95=0.05
Z critical value(using Z table)=1.96
Confidence interval formula is ;
p ± Z * √(p(1-p)/n
= 0.70 ± √(0.7(1-0.7)/130
=(0.6212,0.7788)
Lower confidence interval limit =0.6212
Upper confidence interval limit =0.7788
In percentages , we simply multiply by 100 in both cases =
62.12 % to 77.88%
Given that is both the median and altitude of , congruence postulate SAS is used to prove that is what type of triangle?
A.
equilateral
B.
scalene obtuse
C.
isosceles
D.
scalene acute
Answer:isosceles is the correct
Step-by-step explanation:
According to the given conditions the triangle ABC is an isosceles triangle.
What is an isosceles triangle?An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles ADB and CBD congruent by SAS rule,
So, the proof is as follows,
AD = CD [definition of median]
∠ ADB = ∠ CDB [definition of altitude]
BD = BD [reflexive property]
∴ Δ ADB ≅ Δ CBD by SAS rule
AB = BC by CPCT
According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.
Hence, according to the given conditions the triangle ABC is an isosceles triangle.
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A dress regularly sells for $137. The sale price is $102.75. Find the discount & the percent of the discount
Answer:
Discount : $34.25 off. Percent of the discount : 25%
Step-by-step explanation:
137 - 102.75 = 34.25.
34.25/137 x 100 = 25%
The LARGEST prime number that is less than 100 is
(A) 91
(B) 93
(C) 97
(D) 99
Answer:
97
Step-by-step explanation:
ez
Answer:
(c) 97
Step-by-step explanation:
97 is the largest prime number because 97 has no other multiples other than 1 and itself. 99 is divisible by 3, 9, 11, 33, 99.
91 is a prime number but it is not the greatest.
93 is a composite.
99 is a composite as well.
Multiply the rational expressions: Divide the rational expressions:
Answer:
1). [tex]\frac{2}{(x+1)}[/tex]
2). [tex]\frac{x^2}{2(x+1)}[/tex]
Step-by-step explanation:
For multiplication of the rational expressions,
[tex]\frac{x}{(x+1)}\times \frac{2}{x}[/tex]
= [tex]\frac{2x}{x(x+1)}[/tex]
= [tex]\frac{2}{(x+1)}[/tex]
For division of the rational expressions,
[tex]\frac{x}{(x+1)}\div \frac{2}{x}[/tex]
= [tex]\frac{x}{(x+1)}\times \frac{x}{2}[/tex]
= [tex]\frac{x^2}{2(x+1)}[/tex]
[When the divisor is a rational expression or a rational number, we change the sign from division to multiplication and reciprocate or flip the fraction.
This is applicable for division of the rational expressions only].
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
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Which question is best modeled with a division expression? What is the sum of 3 and StartFraction 8 Over 11 EndFraction? What is the quotient of 3 and StartFraction 8 Over 11 EndFraction? What is the product of 3 and StartFraction 8 Over 11 EndFraction? What is the difference of 3 and StartFraction 8 Over 11 EndFraction?
Answer: B
Step-by-step explanation:
The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The numbers are given below.
3 and 8/11
The sum of the numbers is calculated as,
⇒ 3 + 8/11
⇒ (33 + 8) / 11
⇒ 41 / 11
⇒ 3.7272
The quotient of the numbers is calculated as,
⇒ 3 / (8/11)
⇒ 3 x 11 / 8
⇒ 4.125
The product of the numbers is calculated as,
⇒ (3) x (8 / 11)
⇒ 24 / 11
⇒ 2.1818
The difference between the numbers is calculated as,
⇒ 3 - 8/11
⇒ (33 - 8) / 11
⇒ 25 / 11
⇒ 2.2727
The sum, quotient, product, and difference of the numbers 3 and 8/11 will be 3.7272, 4.125, 2.1818, and 2.2727 respectively.
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[tex]{x}^{ log_{3}(x) } = 81 {x}^{3} [/tex]
can you solve by algebraically, not graphing and provide step by step explanation, please?
Answer:
x=81 or 1/3
Step-by-step explanation:
[tex]x^\log_3(x)} =81x^3\\\log_3(x^{\log_3(x)})=\log_3(81x^3)\\\(\log_3x)(\log_3x)=\log_381+\log_3x^3\\(\log_3x)^2=3\log_3x^+4\\\\Let u=\log_3x\\\\u^2-3u-4=0\\(u-4)(u+1)=0\\u=4 \\4=\log_3x\\x=3^4=81\\\\u=-1\\-1=\log_3x\\x=3^{-1}=1/3[/tex]
The volume of a spherical cancerous tumor is given by the following equation. V(r) =(4/3)pi r^3 If the radius of a tumor is estimated at 1.4 cm, with a maximum error in measurement of 0.005 cm, determine the error that might occur when the volume of the tumor is calculated:___________.
Answer:
The error that might occur is [tex]\±0.123cm^3[/tex]
Step-by-step explanation:
Given
[tex]V = \frac{4}{3}\pi r^3[/tex]
[tex]Radius,\ r = 1.4cm[/tex]
[tex]Error = 0.005cm[/tex]
Required
Determine the error that might occur in the volume of the tumor
Given that there's an error in measurement, this question will be solved using the concept of differentiation;
First, we'll rewrite the given parameters in differentiation notations;
[tex]r = 1.4[/tex] --- Radius
[tex]dV = \±0.005[/tex] --- Change in measurement
[tex]V(r) = \frac{4}{3}\pi r^3[/tex] --- Volume as a function of radius
The relationship between the above parameters is as follows;
[tex]\frac{dV}{dr} = V'(r)[/tex]
This can be rewritten as
[tex]\frac{dV}{dr} = (V(r))'[/tex]
Substitute [tex]\frac{4}{3}\pi r^3[/tex] for [tex]V(r)[/tex]
[tex]\frac{dV}{dr} = (\frac{4}{3}\pi r^3)'[/tex]
Multiply both sides by dr
[tex]dr * \frac{dV}{dr} = (\frac{4}{3}\pi r^3)' * dr[/tex]
[tex]dV = (\frac{4}{3}\pi r^3)' * dr[/tex]
[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]
Differentiate
[tex]dV = \frac{4}{3}\pi( r^3)' dr[/tex]
[tex]dV = \frac{4}{3}\pi* 3r^2\ dr[/tex]
[tex]dV = 4\pi* r^2\ dr[/tex]
Substitute the values of r, dr and take [tex]\pi[/tex] as 3.142
[tex]dV = 4 * 3.142* 1.4^2 * \±0.005[/tex]
[tex]dV = \±0.1231664[/tex]
[tex]dV = \±0.123[/tex] (Approximated)
Hence, the error that might occur is ±0.123
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean pulse rate (in beats per minute) of students in a large math class is greater than 71. A simple random sample of the students has a mean pulse rate of 71.7. Choose the correct answer below.
A. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
Answer:
The correct option is (D).
Step-by-step explanation:
In this case, we need to test whether the mean pulse rate (in beats per minute) of students in a large math class is greater than 71.
The hypothesis can be defined as follows:
H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.
Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.
It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.
The sample mean is not very different from the population mean.
So, it cannot be said in confidence that the sample is unusual.
Thus, the correct option is (D).
"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."
To begin solving this system of linear equations by elimination you can add the equations. 3x + 2y = 38 5x – 2y = -30 8x = 8 This step works because of the A. distributive property B. commutative property 0 0 0 0 O c. multiplication property of equality O D. addition property equality
Answer:D
Step-by-step explanation:
Additive property big brain
This step works because of the addition of property equality.
What is adding the property of equality?The addition property of equality tells us that adding the identical wide variety to each facet of an equation offers us an equal equation. If a−b=c, then a−b+b=c+b,or a=c+b. The same goes with the subtraction belongings of equality
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In order to estimate the average time spent on the computer terminals per student at a university, data were collected for a sample of 81 business students over a one week period. Assume the population standard deviation is 1.8 hours. With a 0.95 probability, the margin of error is approximately
Answer:
The margin of error is approximately 0.39.
Step-by-step explanation:
Formular for the margin of error is
Margin of error = z* (sd/√n)
Where z* is 95% confidence level = 1.96, sd is 1.8 and n is 81
Margin of error = 1.96 (1.8/√81)
= 1.96(1.8/9)
= 1.96*0.2
= 0.392