Answer:
The trip will take 36 minutes.
Step-by-step explanation:
This question can be solved using a rule of three.
The boat maintains a constant speed of 15 knots (nautical miles per hour). How many minutes it will take to return to its home port 9 nautical miles away?
So in 60 minutes, 15 nautical miles. How many minutes for 9 nautical miles?
60 minutes - 15 nautical miles
x minutes - 9 nautical miles
[tex]15x = 60*9[/tex]
[tex]x = \frac{60*9}{15}[/tex]
[tex]x = 36[/tex]
The trip will take 36 minutes.
Can someone help me please
Answer:
the triangles are not similar.
A report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized. Assume that you plan to test the claim that p1=p2. Find the test statistic for the hypothesis test. (Let the houses with the dogs be the first population.)
Answer:
The test statistic for the hypothesis test is -1.202.
Step-by-step explanation:
We are given that a report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized.
Let [tex]p_1[/tex] = population proportion of households with pet dogs who were burglarized.
[tex]p_2[/tex] = population proportion of households without pet dogs who were burglarized.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex] {means that both population proportions are equal}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex] {means that both population proportions are not equal}
The test statistics that would be used here Two-sample z-test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of households with pet dogs who were burglarized = [tex]\frac{10}{129}[/tex] = 0.08
[tex]\hat p_2[/tex] = sample proportion of households without pet dogs who were burglarized = [tex]\frac{23}{197}[/tex] = 0.12
[tex]n_1[/tex] = sample of households with pet dogs = 129
[tex]n_2[/tex] = sample of households without pet dogs = 197
So, the test statistics = [tex]\frac{(0.08-0.12)-(0)}{\sqrt{\frac{0.08(1-0.08)}{129}+\frac{0.12(1-0.12)}{197} } }[/tex]
= -1.202
The value of z test statistics is -1.202.
Solve for m:
-3(1 – 5m) = — 38 + 8m
Answer:
m = - 5
Step-by-step Explanation:
[tex]-3(1-5m)=-38+8m \\ \\ - 3 + 15m = - 38 + 8m \\ \\ 15m - 8m = 3 - 38 \\ \\ 7m = - 35 \\ \\ m = \frac{ - 35}{7} \\ \\ \huge \purple{ \boxed{m = - 5}}[/tex]
Answer:
-5
Step-by-step explanation:
Help on this question please!!!
Answer:
Hello! Here is your answer
Step-by-step explanation:
112=4(28)
a=4b
You can only have one variable so:
Combine b to a:
a-b=84
4b-b=84
Divide both sides by 3:
3b/3=84/3
b=28
But that is not it:
Sum of both cards:
a+b
a=112
b=28
112+28=140
= 140
I hope I was of help. If not please let me know! Thank you! Good luck!
What value of c makes x2 + 6x + c a perfect square trinomial?
Answer:
9
Step-by-step explanation:
x^2 + 6x + c
Take the coefficient of x
6
Divide by 2
6/2 = 3
Square it
3^2 = 9
That is the value of c required
Answer:
C. 9
Step-by-step explanation:
c = 9
x² + 6x + 9
= (x+3)(x+3)
= (x + 3)²
it is a perfect square trinomial when c is equal to 9
Distance between (-6,8) and (-3,9)
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
substitute
[tex]d = \sqrt{((-3) - (-6))^2 + ((9)-(8))^2}[/tex]
[tex]\sqrt{10}[/tex]
On day two of a study on body temperatures, 106 temperatures were taken. Suppose that we only have the first 10 temperatures to work with. The mean and standard deviation of these 10 temperatures were 98.44oF and 0.30oF, respectively. Construct a 95% confidence interval for the mean of all body temperatures.
Answer:
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622
The margin of error is:
M = T*s = 2.2622*0.3 = 0.68
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF
The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
Round 8326 to the nearest hundred
Answer:
The answer is 8300.
Step-by-step explanation:
1) We round the number up to the nearest hundred, if the last two digits in the number are 50 or above.
2) We round the number down to the nearest 100 if the last two digits in the number are 49 or below.
3) If the last two digits are 00, then we do not have to do any rounding because it is already to the hundred.
At a local college, 138 of the male students are smokers and are non-smokers. Of the female students, are smokers and are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Answer:
The probability that both the male and female student are non-smokers is 0.72.
Step-by-step explanation:
The complete question is:
At a local college,178 of the male students are smokers and 712 are non-smokers. Of the female students,80 are smokers and 720 are nonsmokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Solution:
Let, X denote the number of non-smoker male students and Y denote the number of non-smoker female students.
It is provided that:
X' = 178
X = 712
Tx = 890
Y' = 80
Y = 720
Ty = 800
Compute the probability of selecting a non-smoker male student as follows:
[tex]P (\text{Non-smoker Male student})=\frac{712}{890}=0.80[/tex]
Compute the probability of selecting a non-smoker female student as follows:
[tex]P (\text{Non-smoker Female student})=\frac{720}{800}=0.90[/tex]
Compute the probability that both the male and female student are non-smokers as follows:[tex]P(\text{Non-smoker Male and Female})=P(\text{Non-smoker Male})\times P(\text{Non-smoker Female})[/tex]The event of any female student being a non-smoker is independent of the male students.
[tex]P(\text{Non-smoker Male and Female})=0.80\times 0.90[/tex]
[tex]=0.72[/tex]
Thus, the probability that both the male and female student are non-smokers is 0.72.
a)i.Write the the absolute value function y=|2x+5|+3|x-1| as a piece-wise function.
ii)What is the range?
Answer:
Step-by-step explanation:
for |2x+5|=
[tex]\left \{ {{2x+5}~~~~if~~~~2x+5 > 0 ~~or ~~~~x>\frac{-5}{2}~~(case 1) \\ \atop {-2x-5}} ~~~~~if~~~2x+5 <0 ~~~~or~~~x<\frac{-5}{2}~~(case 2)[/tex]
for |x-1| = [tex]\left \{ {{x-1 } ~~~~if~~~x-1>0 ~~~or~~~x>1 ~~(case 3)\atop {1-x}} ~~~~if ~~~~x-1<0 ~~~~or~~~x<1 \right. (case 4)[/tex]
. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
Answer:
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 1/2 = 0.5
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.5 = 0.5
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.5)^8 × (0.5)^2
P(X) = 0.0039 x 0.25
P(X) = 0.00098 = 0.098%
Over which interval is the graph of fx =-x2 + 3x + 8 increasing
Answer:
Step-by-step explanation:
it is increasing in [tex]]-\infty;3/2][/tex]
because this is like
[tex]f(x)=ax^2+bx+c[/tex]
where a > 0
and -b/a=3/2
whatt is the equation of the line that passes through the points (-3,-3) and (3,1)
Answer:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]
And we can use one of the points in order to find the intercept like this:
[tex] -3= \frac{2}{3} (-3) +b[/tex]
[tex] b =-3 +2=-1[/tex]
And the equation would be given by:
[tex] y= \frac{2}{3}x -1[/tex]
Step-by-step explanation:
We want an equation given by:
[tex] y=mx+b[/tex]
where m i the slope and b the intercept
We have the following two points given:
[tex] (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)[/tex]
We can find the slope with this formula:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]
And we can use one of the points in order to find the intercept like this:
[tex] -3= \frac{2}{3} (-3) +b[/tex]
[tex] b =-3 +2=-1[/tex]
And the equation would be given by:
[tex] y= \frac{2}{3}x -1[/tex]
Which graph represents the solution set for
-X2 + 8x - 12 > 0?
Answer:
B
Step-by-step explanation:
A fuel oil tank is an upright cylinder, buried so that its circular top is 8 feet beneath ground level. The tank has a radius of 6 feet and is 18 feet high, although the current oil level is only 12 feet deep. Calculate the work required to pump all of the oil to the surface. Oil weighs 50\, \hbox{lb/ft}^3.
Answer:
1.504×10⁶ ft·lb
Step-by-step explanation:
We understand the top of the oil in the tank is 12 ft below ground level, and the bottom of the tank is 8+18=26 ft below ground level. Then the average depth of the oil is (12+26)/2 = 19 ft below ground level.
The height of the oil in the tank is 26-12=14 ft, so the volume of it is ...
V = πr²h = π(6 ft)²(14 ft) = 504π ft³ ≈ 1583.36 ft³
__
So, the work required to raise that volume of oil to the surface is ...
(1538.36 ft³)(50 lb/ft³)(19 ft) = 1.504×10⁶ ft·lb
if you start with (2,6) and move 2 units right and 3 units down what will you end up with?
For (2,6) the 2 is the x value which is the left/right position and 6 is the y value which is the up/down position.
Moving 2 units to the right, you would add 2 to the x value. Moving 3 units down you would subtract 3 from the y value.
The answer would be (4,3)
A multiple-choice standard test contains total of 25 questions, each with four answers. Assume that a student just guesses on each question and all questions are answered independently. (a) What is the probability that the student answers more than 20 questions correctly
Answer:
[tex]P(x>20)=9.67*10^{-10}[/tex]
Step-by-step explanation:
If we call x the number of correct answers, we can said that P(x) follows a Binomial distribution, because we have 25 questions that are identical and independent events with a probability of 1/4 to success and a probability of 3/4 to fail.
So, the probability can be calculated as:
[tex]P(x)=nCx*p^{x}*q^{n-x}=25Cx*0.25^{x}*0.75^{25-x}[/tex]
Where n is 25 questions, p is the probability to success or 0.25 and q is the probability to fail or 0.75.
Additionally, [tex]25Cx=\frac{25!}{x!(25-x)!}[/tex]
So, the probability that the student answers more than 20 questions correctly is equal to:
[tex]P(x>20)=P(21)+P(22)+P(23)+P(24)+P(25)[/tex]
Where, for example, P(21) is equal to:
[tex]P(21)=25C21*0.25^{21}*0.75^{25-21}=9.1*10^{-10}[/tex]
Finally, P(x>20) is equal to:
[tex]P(x>20)=9.67*10^{-10}[/tex]
Maya is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A has no initial fee but charges 80 cents for every mile driven. Company B charges an initial fee of $65 and an additional cents for every mile driven. For what mileages will Company A charge more than Company B? Use m for the number of miles driven, and solve your inequality for m .
Answer:
m > 82.28
Step-by-step explanation:
Price to Pay (P)
distance (m)
Company A
Pa = 0.80m
Company B
Pb = 65 + 0.01m
Company A charge more than B is written like this
0.8m > 65 + 0.01m
then we can solve this inequality
(0.8 - 0.01)m > 65
0.79m > 65
m > 65/0.79
m > 82.28 miles
so if Maya will go more than 82.28 miles, I suggest Company B is cheaper
Pls help me with this
Answer:
x = 1.5
Step-by-step explanation:
Given
[tex]\frac{x}{2} \geq 0.75[/tex]
[tex]\frac{x}{2} < 2.5[/tex]
Required
Find the value of x.
First, the inequalities need to be rewritten and merged;
if [tex]\frac{x}{2} \geq 0.75[/tex], then
[tex]0.75 \leq \frac{x}{2}[/tex]
Multiply both sides by 2
[tex]2 * 0.75 \leq \frac{x}{2} * 2[/tex]
[tex]1.5 \leq x[/tex]
Similarly;
[tex]\frac{x}{2} < 2.5[/tex]
Multiply both sides by 2
[tex]2 * \frac{x}{2} < 2.5 * 2[/tex]
[tex]x < 5[/tex]
Merging these results together; to give
[tex]1.5 \leq x < 5[/tex]
This means that the range of values of x is from 1.5 to 4.9999....
From the question, x is the smallest rational number; from the range above ([tex]1.5 \leq x < 5[/tex]), the minimum value of x is 1.5 and 1.5 is a rational number;
Hence, x = 1.5
Factories fully 4ab + 8ac
Answer:
Hello!
I believe your answer is:
4a(b+2c)
Step-by-step explanation:
I hope this worked for you! Good luck!
What is the result of adding these two equations? 2x+3y=-5 5x-y=-12
Answer:
[tex]x = \frac{-41}{17} , y = \frac{-1}{17}[/tex]
Step-by-step explanation:
Step(i):-
Given equations are 2 x+3 y=-5 ...(i)
5 x-y=-12 ...(ii)
Multiply equation (ii) by '3'
2 x + 3 y = -5
15 x - 3 y = - 36
17 x = - 41
[tex]x = \frac{-41}{17}[/tex]
Step(ii):-
Substitute [tex]x = \frac{-41}{17}[/tex] in equation (i)
2 ([tex]\frac{-41}{17}[/tex]+3 y=-5
3 y = - 5 + [tex]\frac{82}{17}[/tex]
[tex]3 y = \frac{-85 + 82}{17} = \frac{-3}{17}[/tex]
[tex]y = \frac{-1}{17}[/tex]
The solution of the two equations
( x, y ) = [tex](\frac{-41}{17} , \frac{-1}{17})[/tex]
Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. What will Arun’s total bill be? $10.44 $47.56 $68.44 $76.00
Answer:
The Answer is 68.44. I wish it helpsAnswer:
68.44$
Step-by-step explanation:
x=18*58/100=10.44 $(the tip)
58+10.44=68.44 ( the bill )
pleas guys can you answer this to me
Answer:
what is this boiii?
1. Determine the value of 'p' in the equation 4p = 48
2. Simplify the fraction 60/144
3. What is the surface area of a cube with side lengths of 3cm?
1) sorry i don't know =(
2)- 5/12 is the simplified fraction for 60/144.
3)A=54cm²
Which of the following is true regarding the solution to the logarithmic equation below? log Subscript 2 Baseline (x + 11) = 4. x + 11 = 2 Superscript 4. x + 11 = 16. x = 5. x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 2 x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 4 x = 5 is a true solution because log Subscript 2 Baseline (16) = 4 x = 5 is a true solution because log Subscript 4 Baseline (16) = 2
Answer:
Option C.
Step-by-step explanation:
The given logarithmic equation is
[tex]\log_2(x+11)=4[/tex]
It can be written as
[tex](x+11)=2^4[/tex] [tex][\because log_ax=y\Leftrightarrow x=a^y][/tex]
[tex]x+11=16[/tex]
[tex]x=5[/tex]
Now, to check whether [tex]x=5[/tex] is a true solution or not. Substitute [tex]x=5[/tex] in the LHS of given equation.
[tex]LHS=\log_2(5+11)[/tex]
[tex]LHS=\log_2(16)[/tex]
[tex]LHS=\log_22^4[/tex]
[tex]LHS=4[/tex] [tex][\because log_aa^x=x][/tex]
[tex]LHS=RHS[/tex]
Hence, [tex]x=5[/tex] is a true solution because [tex]\log_2(16)=4[/tex].
Therefore, the correct option is C.
Answer:
C on edge2021
Step-by-step explanation:
Find the balance at the end of 4 years if $10000 is deposited at a rate of 1.5% simple interest
Answer:
$9400
Step-by-step explanation:
1.5x4=6%
100-6=94
0.94x10000=9400
Look at the Picture. Look at the Picture.
Answer:
325 square inches
Step-by-step explanation:
Consider the attachment below for further reference. Ideally we would split this figure into parts, and solve as demonstrated by the attachment. I have labeled each rectangle as rectangle 1, rectangle 2, rectangle 3 etc. ;
[tex]Rectangle 1 Area = 17 in * 5 in = 85 square in\\Rectangle 2 Area = ( 17 in - 5 in ) * 14 in = 168 square in,\\Rectangle 3 Area = ( 12 in - 3 in ) * 8 in = 72 square in\\\\Total Area = 85 + 168 + 72 = 325 square inches[/tex]
Hope that helps!
Answer: The answer is 325 inches.
Step-by-step explanation: You can divide the rectangle into multiple parts and find the areas of those parts and add all the areas together at the end
A local country officials need to calculate the capacity of a large hole for the garbage refuse dump. The dump hole is 250 feet long,120 feet wide and 30 feet deep. What is the capacity of the dump hole in cubic feet.
Answer:
900000cubic feet
Step-by-step explanation:
capacity of dump hole= 250*120*30
= 900000cubic feet
An item is regularly priced at 40$. It is. On sale for 30% off the regular price. How much (in dollars) is discounted from the regular price?
Answer:
Step-by-step explanation:
12$
A study seeks to answer the question, "Does Vitamin C level in the breast milk of new mothers reduce the risk of allergies in their breastfed infants?" The study concluded that high levels of vitamin C (measured in mg) were associated with a 30 percent lower risk of allergies in the infants. In this scenario, "levels of vitamin C (measured in milligrams)" is what type of variable?
Answer:
Quantitative variable
Step-by-step explanation:
The objective in this study is to find the of variable used to conduct the study. The type of variable used to conduct this study is Qualitative variable.
There are majorly two types of variable. These are:
Categorical VariableQuantitative variableCategorical variables are types of variables that are grouped based on some similar characteristics. The nominal scale and the ordinal scale falls under this group of variable.
The nominal scale is an act of giving name to a particular object or concept in order to identify or classify that particular thing.
On the other hand, The ordinal scale possess all the characteristics of nominal scale but here the variables can be ordered. It can be used to determine whether the item is greater or less. It express the indication of order and magnitude.
In Qualitative variables; variables are measured on a numeric scale. From the given question , This type of variable is used to measure the high levels of vitamin C (measured in mg) which were associated with a 30 percent lower risk of allergies in the infants.
The levels of vitamin C could range from 0 mg to certain mg therefore we can measure vitamin C in numerical values of measurement (Quantitative variable).
