Answer: Negative sign
Adding two negative values results in another negative value.
-1.69 + (-1.69) = -3.38
It's like starting $1.69 in debt and then adding 1.69 dollars of more debt. You'll slide further into debt being $3.38 in debt total.
The sign is negative as the value of -1.69 + (-1.69) is -3.38.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-1.69 + (-1.69)
= -1.69 - 1.69
= -3.38
This means,
The sign is negative.
Thus,
The value of -1.69 + (-1.69) is -3.38.
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Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?
iv. Describe how you would guide a JHS student to find the bearing and distance of
Musah’s final point from the centre.
Answer:
ii. 75 steps
iii. 75 steps
iv. 106 steps, and [tex]315^{0}[/tex]
Step-by-step explanation:
Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.
ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;
bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]
To determine distance AB,
[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex] + [tex]/25/^{2}[/tex]
= 25000 + 625
= 3125
AB = [tex]\sqrt{3125}[/tex]
= 55.90
AB ≅ 56 steps
Thus, AC = 50 steps + 56 steps
= 106 steps
From ΔACD,
Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]
⇒ x = 106 × Sin [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance west from centre to final point is 75 steps
iii. From the secon attachment, Musah's distance north, y, can be determined by;
Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]
⇒ y = 106 × Cos [tex]45^{0}[/tex]
= 74.9533
≅ 75 steps
Musah's distance north from centre to final point is 75 steps.
iv. Musah's distance from centre to final point is AC = AB + BC
= 50 steps + 56 steps
= 106 steps
From ΔACD,
Tan θ = [tex]\frac{75}{75}[/tex]
= 1.0
θ = [tex]Tan^{-1}[/tex] 1.0
= [tex]45^{0}[/tex]
Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]
= [tex]315^{0}[/tex]
Multiple-Choice Questions
1. In 1995, Diana read 10 English books and 7 French books. In 1996, she read twice as many French books as English books. If 60% of the books that she read during the 2 years were French, how many English and French books did she read in 1996?
(A) 16
(B) 26
(0) 32
(D) 48
Answer:
(D) 48
Step-by-step explanation:
Let English book = x
Let french book = y
In 1995 x= 10
Y= 7
In 1996
Y = 2x
Total book read in the two years
0.6(Total) = y
0.4(total) = x
We don't know the exact amount of books read in 1996.
Total = 10 + 7 +x +2x
Total = 17+3x
0.6(total) = 7+2x
0.6(17+3x) = 7+2x
10.2 +1.8x= 7+2x
10.2-7= 2x-1.8x
3.2= 0.2x
3.2/0.2= x
16= x
So she read 16 English book
And 16*2 = 32 french book Making it a total of 16+32= 48 books in 1996
Subtract 2x^2 -9x - 7 from 8x^2 -5x + 9.
Answer:
-6x² -4x -16
Step-by-step explanation:
be watchful of signs to avoid making errors
Karl needs a total of $30 to buy a bike. He has $12. He can earn $6 an hour
babysitting. Which equation can be used to find the number of hours, h, Karl has to
babysit to have the money he needs?
30 - 6h + 12 = 0
6+ n = 12
6 + 12 h = 30
6 h + 12 = 30
Answer:
6h + 12 = 30
Step-by-step explanation:
Hence, the equation obtained for number of hours worked is given as 12 + 6h = 30.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
The total money required is given as $30.
Suppose the number of hours for babysitting be h.
Then, the money earned by doing it is $6h.
And, the total money with Karl is 12 + 6h.
As per the question, the following equations can be written as,
12 + 6h = 30
Hence, the equation for finding the number of hours is given as 12 + 6h = 30.
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According to a survey, typical American spends 154.8 minutes per day watching TV. A survey of 50 Internet users results in a mean time watching TV per day of 128.7 minutes, with a standard deviation of 46.5 minutes. Which appropriate test we should use to determine if Internet users spend less time watching TV
Answer:
Z > ± 1.645
z= 3.968
Step-by-step explanation:
We formulate the null and alternate hypotheses as
H0 =μ2 ≥ μ1 Ha: μ2 <μ1 one sided
Let α= 0.05
Since the sample sizes are large therefore the test statistic used under H0 is
The critical region for α= 0.05 for a one tailed test Z > ± 1.645
Z = (x`2- x`1) /s/ √n
Z= 154.8-128.746.5/√50
z= 26.1/6.577
z= 3.968
Since the calculated value of z lies in the critical region we reject H0 that internet users spend more time or equal time.
Su Jean is driving from phoenix to houston. A distance of 1185 miles. After driving for 4 hours she calculates that she has driven 237 miles. What portion of the distance does she have left to drive?
Answer:
4/5
Step-by-step explanation:
237/1185 = .2 = 1/5
meaning there's 4/5 left
Determine whether each equation has one solution, no solution or infinitely many solutions. 4x + 10 = 2(2x + 5) 4x - 5 = 4x + 10 4x - 5 = -5
Answer:
see below
Step-by-step explanation:
4x + 10 = 2(2x + 5)
Distribute
4x+10 = 4x+10
Since the left side is identical to the right side, there are infinite solutions
4x - 5 = 4x + 10
Subtract 4x from each side
-5 = 10
This is never true, so there are no solutions
4x-5 = -5
Add 5 to each side
4x = 0
x=0
There is one solutions
In recent years, the interest rates on home mortgages have declined to less than 6%. However, a
recent study shows that the rate charged on credit card debt is more than 14%. A sample of 10 credit
cards showed that the mean rate charged is 15.64% with a standard deviation of 1.561%. At 1% level
of significance, is it reasonable to conclude the mean rate charged is greater than 14%?
Answer:
Yes it is reasonable to conclude the mean rate charged is greater than 14%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.14[/tex]
The sample size is [tex]n = 10[/tex]
The sample mean is [tex]\= x = 0.1564[/tex]
The standard deviation is [tex]\sigma = 0.01561[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o: \mu = 0.14[/tex]
The alternative hypothesis is [tex]H_a : \mu > 0.14[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]
[tex]t = 3.322[/tex]
Now the p-value obtained from the z-table is
[tex]p-value = P(t > 3.322) = 0.00044687[/tex]
Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that the mean rate charged is greater than 14%
Six people attend the theater together and sit in a row with exactly six seats.
a. How many ways can they be seated together in the row?
b. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people be seated together in the row with the doctor in an aisle seat?
c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?
Answer
A. 720 ways
B. 240 ways
C. 6 ways
There are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
It is assumed that six people will attend the theater together and sit in a row of six.
The following are the various ways they can be seated in a row together:
⇒ 6!
⇒ 6 × 5 × 4 × 3 × 2 × 1
⇒ 720
If the doctor sits in the aisle seat, the remaining 5 persons can sit in the remaining 5 seats 5! ways
The total possibilities are as follows:
⇒ 5 × 4 × 3 × 2 × 1
= 120
Consider that the six persons are made up of three married couples.
In addition to the aforementioned, divide the six chairs into three groups of two seats each.
There is one choice in each block for the husband to be placed on the left and the wife to be positioned on the right and the 3 couples can be seated in the 3 blocks in 3! ways.
⇒ 3 × 2 × 1
The required answer is 6.
Thus, there are 720 ways they can be seated in a row together, 120 ways can the people be seated together in a row with the doctor in an aisle seat, and 6 ways can the six be seated together in a row.
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. One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, what is the value of Cohen’s d?
Answer:
Cohen's d : 1.00
Step-by-step explanation:
We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.
The formula to solve for the value of Cohen's d is as follows,
d = M₁ - M₂ / S - pooled,
d = 18 - 14 / 4 = 4 / 4 = 1
Therefore the value of Cohen's d = 1
Factor 13ab3 + 39a2b5.
[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]
Brazil number one.
Answer:
there's no answer for that equation
If 2x + 5 = 8x, then 12x = ?
A 5
B
10
C
15
D 20
Answer:
10
Step-by-step explanation:
2x + 5 = 8x
Subtract 2x from each side
2x-2x + 5 = 8x-2x
5 = 6x
We want 12x so multiply each side by 2
2*5 = 6x*2
10 = 12x
Answer:
B. 10
Step-by-step explanation:
To find 12x, you first need to find the value of x using the first equation:
[tex]2x+5=8x[/tex]
You need to get the variables (x) on the same side of the equation in order to simplify them. To do this, use reverse operations. Subtract 2x from both sides to keep the equation balanced:
[tex]2x-2x+5=8x-2x\\\\5=6x[/tex]
Now isolate the variable (x) by dividing both sides of the equation by 6 (using reverse operations):
[tex]\frac{5}{6}=\frac{6x}{6} \\\\\frac{5}{6}=x[/tex]
Now insert the given value of x into 12x:
[tex]12(\frac{5}{6})[/tex]
Simplify:
[tex]12*\frac{5}{6} \\\\\frac{12}{1}*\frac{5}{6}\\\\\frac{60}{6}=10[/tex]
12x equals 10.
:Done
75% of this
number is 13.5
Answer:
10.125
Step-by-step explanation:
Hello!
To find this we first have to convert the percentage to a decimal
We do this by moving the decimal point two times left
75.0% = 0.75
Now we multiply this by the number
13.5 * 0.75 = 10.125
The answer is 10.125
Hope this helps!
The solution system to 3y-2x=-9 and y=-2x+5
Answer:
[tex]\boxed{(3,-1)}[/tex]
Step-by-step explanation:
Hey there!
Well to find the solution the the given system,
3y - 2x = -9
y = -2x + 5
So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.
3(-2x + 5) - 2x = -9
Distribute
-6x + 15 - 2x = -9
-8x + 15 = -9
-15 to both sides
-8x = -24
Divide -8 to both sides
x = 3
Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.
y = -2(3) + 5
y = -6 + 5
y = -1
So the solution is (3,-1).
Hope this helps :)
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.) ∫4x2 lnx dx ; u= lnx , dv=4x 2dx
Take
[tex]u=\ln x\implies\mathrm du=\dfrac{\mathrm dx}x[/tex]
[tex]\mathrm dv=4x^2\,\mathrm dx\implies v=\dfrac43x^3[/tex]
Then
[tex]\displaystyle\int4x^2\ln x\,\mathrm dx=\frac43x^3\ln x-\frac43\int x^2\,\mathrm dx=\frac43x^3\ln x-\frac49x^3+C[/tex]
[tex]=\boxed{\dfrac49x^3(3\ln x-1)+C}[/tex]
The required integration is,
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C
The given integral is,
∫4x² lnx dx
Using integration by parts, choose u and dv.
In this case, we choose u = lnx and dv = 4x²dx.
Using the formula for integration by parts, we have:
∫ u dv = uv - ∫ v du
Substituting the values of u and dv, we get:
∫4x² lnx dx = (lnx) (∫ 4x² dx) - ∫ [(d/dx)lnx] (∫4x² dx) dx
Simplifying the first term using the power rule of integration, we get:
∫ 4x² dx = (4/3)x³ + C₁
For the second term, we need to evaluate (d/dx)lnx,
Which is simply 1/x. Substituting this value, we get:
∫ [(d/dx)lnx] (∫4x² dx) dx = ∫ [(1/x) ((4/3)x³ + C₁)] dx
Simplifying this expression, we get:
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - ∫ [(4/3)x³/x] dx
Using the power rule of integration again, we get:
∫4x² lnx dx = (lnx) [(4/3)x³ + C₁] - (4/9)x³ + C
Where C is the constant of integration.
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According to a report in USA Today, more and more parents are helping their young adult children purchase their first home. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion
Answer:
the margin of error
= 1.96 x 0.0632
= 0.124
Step-by-step explanation:
this question has the sample size, n = 40
8 people have received help from their parents from this sample.
8/40 = 0.2
which is the sample proportion
z = 1 - 0.2
= 0.8
to calculate standard error
√pz/n
= √0.2 x 0.8/40
= √0.16/40
= 0.0632
at 95% confidence level
z(alpha/2) = 1.96
therefore the margin of error
= 1.96 x 0.0632
= 0.124
If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill the entire bathtub? Write an equation in one variable to help you solve the problem. The variable represents the unknown time in minutes.
Answer:
2.8
Step-by-step explanation:
Hey there!
Well to find the amount of minutes needed to fill a 46.2 gallon bathtub we’ll divide.
46.2 / 16.5
= 2.8
2.58 minutes
Hope this helps :)
which rate can you set 7 miles over 1 hour equal to in order to find the distance traveled in 49 hours at 7 miles per hour
Answer:
Step-by-step explanation:
time = 49 hours
speed = 7 miles/hour
speed = distance / time
∴ distance = speed × time
= 7 × 49
= 343 miles
A house m by m is surrounded by a walkway m wide. 27 9 1.8 a) Find the area of the region covered by the house and the walkway. b) Find the area of the walkway.
Answer:
A. 385.56 square meters.
B. 142.56 square meters.
Step-by-step explanation:
A house 27m by 9m is surrounded by a walkway 1.8m wide.
a) Find the area of the region covered by the house and the walkway.
b) Find the area of the walkway.
Let
Length of the house=l=27m
Width of the house=w=9m
Wideness of the walkway=x=1.8m
Area of the region covered by the house and the walkway
=( L + 2*x) * (w + 2*x)
= (27+2*1.8)*(9+2*1.8)
=(27+3.6)*(9+3.6)
=(30.6)*(12.6)
=385.56 square meters.
b) Area of the walkway
= (L + 2*x)*(w + 2*x) - l*w
= (27+2*1.8)*(9+2*1.8) - 27*9
=(27+3.6)*(9+3.6) - 243
=(30.6)*(12.6) - 243
=385.56 - 243
=142.56 square meters.
What is the value of the mean from the following set of data: 12,10, 11, 8, 6, 5, 3, 7, 9. Round to the nearest hundredth.
Answer:
7.88 or 7.9
Step-by-step explanation:
To find the mean, we need to do:
=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9
=> 71/9
=> 7.88 or 7.9
I divided the sum of all numbers by 9 because we added 9 numbers.
how do you figure out ratios? the problem is 12 quarters to 34 dollars. thanks
Step-by-step explanation:
When you have a ratio, you put one number as the numerator and than one number as the denominator.
so it would be (12/34)=(x/68)
In this example I made the ratio you are comparing it to have 68 dollars, so when you solve for the amount of quarters you need it should be 24, since all of the numbers in this example are just being doubled.
To solve for x, you multiply 68 on both sides of the equation, 68×(12/34)=x
24=x
So this proves that this is how ratios, are used. It also does not matter what number you place on the numerator or denominator.
A population of values has a normal distribution with μ= 106.9 and σ=14.5
You intend to draw a random sample of size n=20
What is the probability that a single randomly selected value is less than 109.8?
P(X < 109.8)
How do you the probability that a sample of size n= 20 is randomly selected with a mean less than 109.8?
P(M < 109.8)
Also, I have to round the answer to the 4th decimal place. How do I do that?
Step-by-step explanation:
Find the z-score.
z = (x − μ) / σ
z = (109.8 − 106.9) / 14.5
z = 0.2
Use a chart or calculator to find the probability.
P(Z < 0.2) = 0.5793
Find the mean and standard deviation of the sampling distribution.
μ = 106.9
σ = 14.5 / √20 = 3.242
Find the z-score.
z = (x − μ) / σ
z = (109.8 − 106.9) / 3.242
z = 0.894
Use a calculator to find the probability.
P(Z < 0.894) = 0.8145
Which polynomial is prime? x2 + 9 x2 – 25 3x2 – 27 2x2 – 8
This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).
Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.
Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.
Answer:
A
Step-by-step explanation:
because it has a + sign
Hi people if someone gives me a hint please. Show algebraically that the product of two consecutive numbers is always even l wrote n (n+1) is always an even number But doesnt recognise it as 100% right thanks for any help
Step-by-step explanation:
Consider the following rules.
even + odd = odd
even - odd = odd
even × odd = even
even ÷ odd = even (if divisible)
Now for the two consectives terms...
One will surely be even and the other, odd.
So using the rule
Their product will always be odd
Hope it helps....
BRAINLIEST PRETTY PLEASE!!
Please help, thanks!!!!!
Answer:
[ 2+0+8. 0+0+12][-4+10+2. 0+25+3]
[10. 12]
[8. 28]
Option 3 is the solution
[tex]f(x) = sqr root x+3 ; g(x) = 8x - 7[/tex]
Find (f(g(x))
[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]
Which point slope form equations could be produced with the points (3,2) and (4,6)
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of a line given two points first find the slope of the line and use the formula
y - y1 = m( x - x1) to find the Equation of the line using any of the points given
Slope of the line using points
(3,2) and (4,6) is
[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]
So the equation of the line using point
( 3 , 2 ) and slope 4 is
y - 2 = 4( x - 3)Hope this helps you
Given a dataset with the following properties:
mean = 50
median = 40
standard deviation = 5
What is the shape of the distribution?
Answer:
The distribution is positively skewed.
Step-by-step explanation:
A measure of skewness is defined in such a way that the measure should always be zero when the distribution is symmetric and measure should be a pure number i.e independent of origin and units of measurement.
The shape of the distribution can be found by finding the coefficient of skewness.
The coefficient of skewness can be found by
Sk= 3(Mean-Median)/ Standard Deviation
Sk= 3( 50-40)5= 30/5=6
The shape will be positively skewed.
In a positively skewed distribution the mean > median > mode. It has a long right tail.
Using the skewness formula, it is found that the distribution is right-skewed.
------------------
The skewness of a data-set with mean M, median [tex]M_e[/tex] and standard deviation s is given by:[tex]S = \frac{3(M - M_e)}{s}[/tex]
If |S| < 0.5, the distribution is said to be symmetric.If S <-0.5, the distribution is left-skewed.If S > 0.5, the distribution is right-skewed.------------------
Mean of 50, thus, [tex]M = 50[/tex]Median of 40, thus [tex]M_e = 40[/tex]Standard deviation of 5, thus, [tex]s = 5[/tex]The coefficient is:
[tex]S = \frac{3(M - M_e)}{s} = \frac{3(50 - 40)}{5} = \frac{30}{5} = 6[/tex]
Thus, the distribution is right-skewed.
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The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is not information about the proportion of students who might choose the option. What size sample should the department head take if he wants to be 95% confident that the estimate is within 0.10 of the true proportion
Answer:
96
Step-by-step explanation:
From the given information:
At 95% Confidence interval level,Level of significance [tex]\alpha[/tex] 0.05, the value of Z from the standard normal tables = 1.96
Margin of Error = 0.10
Let assume that the estimated proportion = 0.5
therefore; the sample size n can be determined by using the formula: [tex]n =(\dfrac{Z}{E})^2 \times p\times (1-p)[/tex]
[tex]n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)[/tex]
[tex]n =(19.6)^2 \times 0.5\times (0.5)[/tex]
n = 96.04
n [tex]\approx[/tex] 96
Identify which equations have one solution, infinitely many solutions, or no solution. No solution: One solution: Infinitely solution:
Answer:
Top left: no
Top middle: one
Top right: no
Bottom left: infinite
Bottom middle: one
Bottom right: one
Step-by-step explanation:
Top left: no
Top middle: one
Top right: no
Bottom left: infinite
Bottom middle: one
Bottom right: one
