Answer:
Step-by-step explanation:
The square root of 7066 is 84.0595....
Therefore the largest number we must test is 84, seeing as now we have proven we do not need to test any numbers greater than 84.0595...
That means, we only need to test prime numbers smaller than 84 to see if they go into 7066.
84 isn't prime. But 83 is prime.
Therefore, the greatest prime that needs to be considered for divisibility is 83.
Answer:
The numbers 7066 is not prime .
But we easily know when a number is prime when we divide it by the first prime numbers; 2, 3, 5, 7, 11.
Step-by-step explanation:
It is known with certainty that a number is prime when it is only divisible by and by unity.
But in this case, that number, when divided by other numbers less than the one, shows that when dividing into the remainder, it gives zero, which means that it is not only divisible by itself or by the unit, but also by other numbers.
for example; 7066/2=3533 , the remainder is zero;
Brenda is going from $(-4,5)$ to $(5,-4)$, but she needs to stop by the origin on the way. How far does she have to travel?
Answer:
[tex]\boxed{D = 6.4 units}[/tex]
Step-by-step explanation:
She stops by (0,0)
She further needs to travel to (5,-4)
Let's calculate the distance using the Distance Formula:
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
D = [tex]\sqrt{(5-0)^2+(-4-0)^2}[/tex]
D = [tex]\sqrt{(5)^2+(-4)^2}[/tex]
D = [tex]\sqrt{25+16}[/tex]
D = [tex]\sqrt{41}[/tex]
D = 6.4 units
She needs to travel 6.4 units more.
Answer:
2sqrt41
Step-by-step explanation:
Origin=(0,0)
Brenda wants to go from (-4,5) to (0,0) and then to (5,-4). So we need to calculate the distance from (-4,5) to (0,0), and the distance of (0,0) to (5,-4).
The distance formula is sqrt (x2-xs1)^2+(y2-y1`)^2.
So: sqrt (5-0)^2+(-4-0)^2
sqrt (5^2+-4^2)
sqrt 25+16
sqrt 41
Now we need to figure out the distance from (0,0) to (5,-4)
sqrt(0-5)^2+(0-(-4))^2
sqrt(-5^2+4^2)
sqrt 25+16
sqrt 41
sqrt 41+sqrt 41
2sqrt41
Sum of two consecutive integers is -221
Answer:
-111 and -110
Step-by-step explanation:
If x is the lesser integer, and x+1 is the next integer, then:
x + x+1 = -221
2x = -222
x = -111
x+1 = -110
The two integers are -111 and -110.
Answer:
-111,-110
Step-by-step explanation:
Let n represent the first integer. Then n+1 will represent the next consecutive integer.
Translate into an equation.
We can restate the given information in one sentence as "The sum of the integers is −221."
As an equation this sentence is represented as:
n+n+1=−221
Solve the equation.
n+n+1=-221
2n+1=−221
2n=−222
n=−111
So, n=−111 is the first integer and n+1=−110 is the second integer.
Urelia made a deposit to her checking account. She had $104.00 in currency; $7.64 in coins; and checks for $83.29, $257.77, $1,332.68, and $3,984.05. What was her total deposit?
Help pls!!!!!!!!!!!!!!!!!!!!!!!!!!♥️
Answer:
A
Step-by-step explanation:
Identify the P-VALUE used in a hypothesis test of the following claim and sample data:
Claim: "The proportion of defective tablets manufactured in this factory is less than 6%."
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective. Test the claim at the 0.05 significance level.
Answer:
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
Step-by-step explanation:
Step(i):-
Given Population proportion P = 0.06
Sample size 'n' = 500
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective.
Sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{20}{500} =0.04[/tex]
Null hypothesis :H₀: P = 0.06
Alternative Hypothesis :H₁:P<0.06
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }[/tex]
[tex]Z = \frac{0.04 -0.06}{\sqrt{\frac{0.06 X 0.94}{500} } }[/tex]
Z = - 2
|Z|= |-2| = 2
Step(iii):-
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
Match the information on the left with the appropriate equation on the right.
Answer:
Step-by-step explanation:
1). Equation of a line which has slope 'm' and y-intercept as 'b' is,
y = mx + b
If slope 'm' = 1 and y-intercept 'b' = -3
Equation of the line will be,
y = x - 3
x - y = 3
2). Equation of a line having slope 'm' and passing through a point (x', y') is,
y - y' = m(x - x')
If the slope 'm' = 1 and point is (-1, 2),
The the equation of the line will be,
y - 2 = 1(x + 1)
y = x + 1 + 2
y = x + 3
x - y = -3
3). Equation of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,
[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]
If this line passes through (-2, 3) and (-3, 4),
[tex]y-3=\frac{(4-3)}{(-3+2)}(x+2)[/tex]
y - 3 = -1(x + 2)
y = -x - 2 + 3
y = -x + 1
x + y = 1
Help ASAP
Picking the first second and third place winners at a track meet is an independent event.
False
Or
True
false, an independent event is an event that isn't affected
The statement given is false
What is a dependent event?
Two events are dependent, when the outcome of the first event influences the outcome of the second event.
Given that, Picking the first second and third place winners at a track meet is an independent even,
This statement is not correct.
The event is a dependant variable, the 1st person is picked based on the 1st mark on the track, so is the second and the 3rd. their position influence the outcome of the other.
the position of the 1st, 2nd or 3rd is influenced by time and speed, so the positions will be picked based on the participant scores /effect of time or speed of the 1st person to reach the track meet.
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Convert the measurement. Use unit fractions or the metric conv
38 L to mL
38 L =
mL. (Type a whole number or a decimal.)
a man is 3 times as old as his son . the sum of their ages is 48 years .how old is the son ? how old is the dad?
Answer:
son is 12
dad is 36
Step-by-step explanation:
Say the son is x years old.
Then the father is 3x. Also 3x+x must be 48.
So 4x = 48 => x= 48/4 = 12
Let x be how old the son is. We know that the dad is 3 times older and their sum is 48. Creating an equation to represent this situation gives us:
[tex]x+3x=48[/tex]
[tex]4x=48[/tex]
Divide both sides by 4
[tex]x=12[/tex]
The son is 12 years old, but we want to find the age of the dad. Since we know the dad is 3 times older, multiply 12 with 3
[tex]12 \times 3 = 36[/tex]
The dad is 36 years old. Let me know if you need any clarifications, thanks!
A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is
Answer:
The correct answer will be "56".
Step-by-step explanation:
Use a combination of 8 things taken 3 at a time :
⇒ [tex]8_{C_{3}}[/tex]
⇒ [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]
⇒ [tex]\frac{8!}{(3!5!)}[/tex]
⇒ [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]
⇒ [tex]8\times 7[/tex]
⇒ [tex]56[/tex]
Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.
Using the principle of combination :
nCr = [n! ÷ (n-r)! r!]Hence, we have ;
8C3 = [8! ÷ (8 - 3)! 3!]
8C3 = [8! ÷ 5!3!]
8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)
8C3 = 8 × 7
8C3 = 56
Hence, there are 56 different possible samples.
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Which of the following is a rational function?
F(x)=8x^2-21x+45
F(x)= 3 root of X +17
F(x)= 16x
F(x)= 5x/x^2-25
Five less than the product of 14 and Vanessa's height Use the variable v to represent Vanessa's height.
Answer:
14v - 5
Step-by-step explanation:
The product of 14 and v is 14v. 5 less than that is 14v - 5.
Answer:
7v = 119
Step-by-step explanation:
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answer:
[tex]\approx[/tex] 17.5% per annum
Step-by-step explanation:
Given:
Money invested = $20,000 at the age of 20 years.
Money expected to be $500,000 at the age of 40.
Time = 40 - 20 = 20 years
Interest is compounded annually.
To find:
Rate of growth = ?
Solution:
First of all, let us have a look at the formula for compound interest.
[tex]A = P \times (1+\frac{R}{100})^T[/tex]
Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.
Here, We are given:
P = $20,000
A = $500,000
T = 20 years
R = ?
Putting all the values in the formula:
[tex]500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%[/tex]
So, the correct answer is [tex]\approx[/tex] 17.5% per annum and compounding annually.
Answer:
16.1%
Step-by-step explanation:
(the other person is wrong, trust me)
6 ≤ x+ 15 plzzzzz helpppp
Answer:
[tex]\large \boxed{\sf \ \ x \geq -9 \ \ }[/tex]
Step-by-step explanation:
Hello, please find below.
[tex]6\leq x+15\\\\\text{*** subtract 15 from both sides ***}\\\\6-15=-9\leq x \\\\x \geq -9[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A researcher wants to study the relationship between salary and gender. She randomly selects 297 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?
Answer:
The researcher cannot conclude that salary and gender are dependent.
Step-by-step explanation:
A dependent variable is a variable, for example "Salary" that depends on an independent variable, e.g. "Gender." Salary is the dependent variable while gender is the independent variable. This means that the value of salary changes in relation to the gender and not vice versa. Two variables become dependent if they change based on another independent variable that is operating on them. In this research, the researcher is not trying to measure gender but the relationship between salary and gender. To achieve her purpose, she shows that salary depends on gender and not that gender depends on salary.
3 sides of the triangle are distinct perfect squares. What is the smallest possible perimeter of the triangle?
Answer:
77
Step-by-step explanation:
At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.
Answer:
e
Step-by-step explanation:
e
What is heron's formula
Answer:
[tex]\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
Step-by-step explanation:
We can use Heron’s formula to determine the area of a triangle when three side lengths of a triangle are given.
[tex]s=\frac{a+b+c}{2}[/tex]
[tex]s : \mathrm{semi \: perimeter}[/tex]
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]A : \mathrm{area}[/tex]
Answer:
Heron's formula gives the area of a triangle when the length of all three sides are known. Use Heron's formula to find the area of triangle ABC, if AB=3,BC=2,CA=4 . Substitute S into the formula . Round answer to nearest tenth.
Step-by-step explanation:
h
e
l
p
?
p
l
e
a
s
e
To clear the fractions we multiply both sides by the least common multiple of all the denominators.
1/2 x + 2/3 = 4
Denominators 2 and 3, so multiply both sides by [Answer]: 6
3/4 x + 1 = 5/6
Denoms 4 and 6, LCM=12 Answer: 12
6/7 x - 2/3 = 5/21
LCM(7,3,21)=21 Answer: 21
3/5 + x/2 = 9
LCM(5,2) Answer: 10
25/4 = 6 + 1/2 x
LCM(4,2) Answer: 4
Please answer this correctly without making mistakes Please simplify the correct answer
Answer:
1/5 are towboats
Step-by-step explanation:
In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together
30k + 10k + 10k= 50k
In total there are 50,000 flag vessels
Of those 50,000, 10,000 of them are tow boats
10,000/50,000 can be simplified to 1/5
1/5 are towboats
Answer:
1/5
Step-by-step explanation:
Well to find the fraction we first need to know the total amount of Flag Vessels.
30,000 + 10,000 + 10,000 = 50,000
If there are 10,000 towboats we can make the following fraction.
10,000/50,000
Simplified
1/5
Thus,
the answer is 1/5.
Hope this helps :)
Solve: 0.1m−1.3m=−2.1−2.7.
Answer:4
Step-by-step explanation:
Simplify what you can which is 0.1m-1.3m
you end up getting -1.2m
Now do the other side of the equation which is 2.1-2.7 which is -4.8
Divide -4.8 by -1.2 to get m=4
Answer: m=4
Step-by-step explanation:
[tex]0.1m-1.3m=-2.1-2.7[/tex]
add like terms
[tex]-1.2m=-2.1-2.7[/tex]
subtract
[tex]-2.1-2.7=-4.8[/tex]
[tex]-1.2m=-4.8[/tex]
multiply both sides by 10
[tex]-12m=-48[/tex]
divide -12 on both sides
m=4
Mikayla asked 10 of her friends how many hours of TV they watch in a week. Three of her friends said 8 hours, two of
her friends said 9 hours, two of her friends said 11 hours, one of her friends said 12 hours, and two of her friends said
14 hours. Mikayla wanted to make a dot plot of the data she gathered. In what order would she create the dot plot?
Draw a number line from 8 to 14. Show the frequency of each number. Title the dot plot.
Show the frequency of each number. Title the dot plot. Draw a number line from 8 to 14.
Title the dot plot. Show the frequency of each number. Draw a number line from 8 to 14.
<-------------------------------------------------->
8 9 10 11 12 13 14 (number of hours spent)
dot plot
Answer:
(A) Draw a number line from 8 to 14. Show the frequency of each number. Title the dot plot.
Step-by-step explanation:
An article reports that when each football helmet in a random sample of 34 suspension-type helmets was subjected to a certain impact test, 24 showed damage. Let p denote the proportion of all helmets of this type that would show damage tested in the prescribed manner.
Required:
a. Calculate a 99% Cl for p.
b. What sample size would be required for the width of a 99% Cl to beat most .10, irrespective of p ?
Answer:
a
[tex]0.5043 < p <0.9075[/tex]
b
[tex]n = 24[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 34
The number of damaged helmets is x = 24
Now the proportion of damaged helmets is mathematically represented as
[tex]\r p = \frac{k}{n }[/tex]
substituting values
[tex]\r p = \frac{24}{34 }[/tex]
[tex]\r p = 0.7059[/tex]
Given that the confidence level is 99% the level of significance can be evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining critical values of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error
The margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p ( 1 - \r p)}{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \sqrt{\frac{ 0.7059 ( 1 - 0.7059)}{34} }[/tex]
[tex]MOE =0.2016[/tex]
The 99% confidence interval for p is mathematically represented as
[tex]p-MOE < p < p + MOE[/tex]
substituting values
[tex]0.7059 - 0.2016 < p <0.7059 + 0.2016[/tex]
[tex]0.5043 < p <0.9075[/tex]
The sample size required for the width of a 99% Cl to beat most 0.10, irrespective of p ? is mathematically represented as
[tex]n \ge \frac{ Z_{\frac{\alpha }{2} } * \sqrt{\r p (1- \r p )} }{\frac{\sigma }{2} }[/tex]
Here [tex]\sigma = 0.10[/tex] telling us that the deviation from the sample proportion is set to 0.10 irrespective of the value of [tex]\r p[/tex]
so the sample size for this condition is
[tex]n \ge \frac{ 2.58 * \sqrt{ 0.7059 (1- 0.7059)} }{\frac{0.10 }{2} }[/tex]
[tex]n \ge 23.51[/tex]
=> [tex]n = 24[/tex]
HELP! WILL GIVE BRAINLIEST!
Answer:
Her eye discourses; I will answer it.
I am too bold; ’tis not to me she speaks:
Two of the fairest stars in all the heaven,
Having some business, do entreat her eyes
To twinkle in their spheres till they return.
Step-by-step explanation:
Which statement describes the order of rotational symmetry for an isosceles triangle?
Answer: it should be b, 1. :)
Step-by-step explanation:
A car started from town p and travelled towards town Q at 70 km/h. at the same time a van started from town Q and travelled to town p at 60km/h after 11/4 hours they were 65 km apart ,still travelling toward each other
Answer:
422.5km
Step-by-step explanation:
Car A started from point P to point R in 11/4hrs by the speed of 70km/hr
Distance = speed × time
= 70×11/4
= 770/4
= 192.5km
Car B
Started from point R and headed to point S in 11/4 hrs by speed of 60km/hr
Distance travelled = speed × time
= 60× 11/4
= 660/4
= 165km
Distance travelled from P to Q
= PR+RS+SQ
= 192.5+65+165
= 422.5km
The average college lecture hall (auditorium) can seat 60 students with a standard deviation of 21. Assume that a total of 60 lecture halls are selected for a sample. What is the standard deviation for the sample mean?
Answer:
The standard deviation of the sample mean is [tex]\sigma _ {\= x } = 2.711[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 60[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
The sample size is [tex]n = 60[/tex]
Generally the standard deviation of the sample mean is mathematically represented as
[tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]
[tex]\sigma _ {\= x } = 2.711[/tex]
on a map 1 inch represents 4 miles how many miles are represented by 3-1/2 ?
Answer:
10 miles
Step-by-step explanation:
1 inch = 4 miles
3 - 0.5 = 2.5
2.5 * 4 = 10 miles
What is the vertex of this parabola y=-5x^2-10x-13
Step-by-step explanation:
Vertex for your equation is (-1, -8)
What is the area of the shaded region? 21 mm2 24 mm2 42 mm2 48 mm2
Answer:
B or 24 mm2
Step-by-step explanation:
Just did the test :)
The area of the shaded region is 24mm^2
What is the area of triangle?Let b be the base and h be the height of the triangle. The area of the triangle is given by bh/2 square units.Step 1: Find area of the larger triangle
Here base b = 5 mm
Height h = 12 mm
Area of the larger triangle = (5*12)/2 = 60/2 = 30mm^2
Step 2: Find area of the smaller triangle
Here base b = 3 mm
Height h = 4 mm
Area of the smaller triangle = (3*4)/2 = 12/2 = 6 mm^2
Step 3: Find area of the required shaded region
Area of the required shaded region = Area of larger triangle - Area of smaller triangle
= 30 mm^2 - 6 mm^2
=24 mm^2
Hence, the area of the shaded region is 24mm^2
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The contingency table represents a box of cards. Box of Cards 1 2 3 4 5 Total Black 1 1 1 1 1 5 Red 1 1 1 0 0 3 Total 2 2 2 1 1 8 What is the probability that a card chosen at random is black and 1?
Answer:
[tex]Probability = \frac{1}{8}[/tex]
Step-by-step explanation:
Given
Box of Cards -- 1 -- 2 -- 3 -- 4 -- 5 -- Total
Black --------------1 ---1 ----1 ----1 ---1 ----5
Red ---------------- 1 ---1 ----1 ----0--- 0--- 3
Total --------------- 2 ---2 --2-----1 -----1 ---8
Required
Determine the probability of a card being black and being card 1
To solve this, we the the number of card 1 that is black
This is shown below
Box of Cards -- 1
Black --------------1
This implies that, 1 card is black and also card 1
Represent this with [tex]n(Black\ and\ 1)[/tex]
[tex]n(Black\ and\ 1) = 1[/tex]
Next, is to get the total number of cards
From the given parameters;
[tex]Total = 8[/tex]
The probability is calculated as follows
[tex]Probability = \frac{n(Black\ and\ 1)}{Total}[/tex]
[tex]Probability = \frac{1}{8}[/tex]