Answer:
49
Step-by-step explanation:
The greatest common divisor of the addends must also be a divisor of 2009. That number can be factored as ...
2009 = 1×2009 = 7×287 = 41×49
The largest possible factor such that the other factor can be a sum of 9 positive integers is 49.
The maximum value of the GCD is 49.
Eric works for salary of $3,500 per month. He has federal income withheld at the rate of 15%, Social Security tax at the rate of 6.2%, Medicare tax at the rate of 1.45% and health insurance premiums of $48 per month. Erik also contributes to a savings plan. Each month, 2% of his gross pay is placed in the savings plan.
After Erik pays the taxes on his money what is Eric's net pay?
A. (1,448.45)
B. (1,799.05)
C. (2,589.25)
D. (2799.05)
Answer:
C. 2,589.25
Step-by-step explanation:
Salary=$3500
Less:
Federal income withheld
15% of $3500
=15/100×$3500
=$525
Social security tax of 6.2%
6.2% of $3500
=6.2/100 × $3500
=$217
Medicare tax of 1.45%
1.45% of $3500
1.45/100 × $3500
=$50.75
Health insurance premium=$48
Savings plan of 2%
2% of $3500
=2/100 × $3500
=$70
Total less:= $525 + $217 + $50.75 + $48 + $70
Eric's net pay =$3500 - $910.75
=$2,589.25
Answer:
c
Step-by-step explanation:
Triangle ABC is drawn inside regular hexagon ABCDEF. What is the ratio of the area of triangle ABC to the area of the hexagon?
The sides of the regular hexagon ABCDEF can be posed as a. If so, the area of ABCDEF should be 6 times the are of the interior angle in the hexagon, considering there are 6 equilateral triangle that can fit in this regular hexagon,
Area = 6( a * a * sin 60 ) / 2,
Area = ( About ) 2.6 sq units
Now applying cosine for triangle ABC -
AC^2 = AB^2 + BC^2 – ( 2*AB*BC*cos 120 ),
a^2 + a^2 – ( 2a^2 * ( - 0.5 ) ) = a^2 + a^2+a^2 =3a^2,
AC = a√3
The area of ABC should thus be the following -
( a√3 * a√3 * sin 60 )/2 = 1.299038106 sq units
As you can see, the area of ABC is half the area of ABCDEF, thus the ratio of the area of ABC to ABCDEF is 1 : 2
Answer:
3.5 units
Step-by-step explanation:
The additive inverse of x/y is
Answer
The additive inverse is
-x/-y
That is equal to x/y
hope this may help you
What is the perimeter of the equilateral triangle if one side is 6 feet?
Answer:
18 feet
Step-by-step explanation:
Equilateral triangles have 3 equal sides.
If one side is 6 feet, the other two are also 6 feet.
Perimeter is all the sides added.
6 + 6 + 6
= 18
The most appropriate measure of center for this
data is the median
Weight of Male Dogs (lb)
4
5
COMPLER
5
2
2
Which statement about the data is true?
The mean is greater than the median
X The mean is equal to the median
* The mean is less than the median
What is the median of the data
Answer:
65
Step-by-step explanation:
45, 50, 52, 58, 62, 68, 72, 78, 81, 95
62 + 68 = 130/2 = 65
The median is 65
Answer:
The median of the data is 65
Step-by-step explanation:
I did it on edge and got it right
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
Answer:
T < -25
Step-by-step explanation:
Was correct on TTM
A metal alloy is 27% copper. Another metal alloy is 52% copper. How much of each should be used to make 22 g of an alloy that is 36.09% copper?
Answer:
14.0008 grams of 27% and 7.9992 grams of 52%
Step-by-step explanation:
We know that in the end we want 22 grams of 36.09% copper, meaning in the end we want 36.09% of the 22 grams to be copper. This means we can multiply 36.09% by 22 to see how much copper we want in the end.
To find out how much of each alloy to use, we can multiply the percentage of copper in the alloy be a variable x, which will be how much of that alloy we use. For the other alloy, we can multiply the percentage by (22-x) grams as we know in the end we want 22 grams and if x+y=22, than y would equal 22-x, and in this case this simplifies it to only use a single variable.
Now finally, making the equation we get 27x+52(22-x)=36.09(22). We can solve this and get 27x+1144-52x=793.98, then combine like terms and get -25x+1144=793.98. Next you have to subtract 1144 from both sides to get -25x=-350.02. Dividing both sides by -25 we get x=14.0008. This is how many grams of 27% copper was used. Now we can subtract this from 22 to get how much 52% copper was used, and we get 22-14.0008=7.9992 grams of 52% copper.
1. 21 + x = 26
2. 12 + 2x = 16
3. 4x - 2 = 10
4. x + 7 = 12
algebra I hat it please help me
Answer:
hope it will help uh ...u will slowly get over it..
5. Which of the following is an equivalent form of the parabola y = x - 4x - 12 that displays
the x-intercepts?
A) y + 12 = x² - 4x
B) y = (x - 2)2 - 16
C) y=(x-6) (x + 2)
D) y = x (x – 4) - 12
Answer:
Your answer is B. Tell me if you need graphics)
it would be C
My best assumption here is you misplaced x^2 in this function. Mostly what is done with the answer C is the function is being FACTORED, and broken down into its simplest form.
5/6-2/7 the answer isnt 23/42 or 8/21
Answer:
Common denominator - 42
Step-by-step explanation:
6 - 6, 12, 18, 24, 30, 36, 42
7 - 7, 14, 21, 28, 35, 42
Hope this helps! :)
Vector A has components (5,6) and vector B has components (-12, 3). What is the direction of the vector C
Vector A has components (5,6) and vector B has components (-12, 3). What is the direction of the vector C = 2A - B
Answer:
22.24° to the positive x-axis.
Step-by-step explanation:Given vectors:
A (5, 6)
B (-12, 3)
C = 2A - B ------------(i)
First let's represent the two vectors in unit notation as follows;
A = 5 i + 6 j
B = -12 i + 3 j
Now substitute these vectors into equation (i) as follows;
C = 2(5 i + 6 j) - (-12 i + 3 j)
C = 2(5 i + 6 j) + (12 i - 3 j)
C = 10 i + 12 j + 12 i - 3 j [collect like terms]
C = 10 i + 12 i + 12 j - 3 j
C = 22 i + 9 j ----------------(ii)
The direction, θ, of vector C can be calculated as follows;
θ = tan⁻¹([tex]\frac{9}{22}[/tex])
θ = tan⁻¹(0.409)
θ = 22.24°
Since both the x and y components of vector C are positive, the direction of the vector is 22.24° to the positive x-axis.
check all that apply
Answer: B & C
Step-by-step explanation:
Putting the values of x & y in all 4 equations we see that the values satisfy equations B & C only. Hence B & C are correct answers
A survey was taken of students in math classes to find
out how many hours per day students spend on social
media. The survey results for the first-, second-, and
third-period classes are as follows:
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3,0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3
Which is the best measure of center for second period
and why?
translate the sum of x and one half of x into a mathematical expression
Answer:
The above statement is written as
[tex]x + 1 \times \frac{1}{2} of \: x[/tex]
of means multiplication
So the final answer is
[tex]x + \frac{3}{2} x[/tex]
Hope this helps you.
Consider the following results for two independent random samples taken from two populations.
Sample 1 Sample 2
n1 = 50 n2 = 35
X1 = 13.6 X2 = 11.6
1 = 2.2 1 = 3.0
1. What is the point estimate of the difference between the two population means?
2. Provide a 90% confidence interval for the difference between the two population means (to 2 decimals).
3. Provide a 95% confidence interval for the difference between the two population means (to 2 decimals).
Answer:
1. Point estimate Md = 2
2. The 90% confidence interval for the difference between means is (1.01, 2.99).
3. The 95% confidence interval for the difference between means is (0.82, 3.18).
Step-by-step explanation:
a) The point estimate of the difference between the two population means is the difference between sample means:
[tex]M_d=M_1-M_2=13.6-11.6=2[/tex]
2. We have to calculate a 90% confidence interval for the difference between means.
The sample 1, of size n1=50 has a mean of 13.6 and a standard deviation of 2.2.
The sample 2, of size n2=35 has a mean of 11.6 and a standard deviation of 3.
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{50}+\dfrac{3^2}{35}}\\\\\\s_{M_d}=\sqrt{0.097+0.257}=\sqrt{0.354}=0.5949[/tex]
The degrees of freedom for this confidence interval are:
[tex]df=n_1+n_2-2=50+35-2=83[/tex]
The critical t-value for a 90% confidence interval is t=1.663.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.663 \cdot 0.5949=0.99[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 2-0.99=1.01\\\\UL=M_d+t \cdot s_{M_d} = 2+0.99=2.99[/tex]
The 90% confidence interval for the difference between means is (1.01, 2.99).
2. We have to calculate a 95% confidence interval for the difference between means.
The critical t-value for a 95% confidence interval and 83 degrees of freedom is t=1.989.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.989 \cdot 0.5949=1.18[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 2-1.18=0.82\\\\UL=M_d+t \cdot s_{M_d} = 2+1.18=3.18[/tex]
The 95% confidence interval for the difference between means is (0.82, 3.18).
4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.
Answer:
Step-by-step explanation:
in x²+y²+2gx+2fy+c=0
center=(-g,-f)
radius=√((-g)²+(-f)²-c)
if center is not changed ,then c will change .
Here only coefficients of E will change.
Find the area of the irregular figure. Round to the nearest hundredth.
Answer:
23.14
Step-by-step explanation:
Solve for the area of the figure by dividing it up into parts. You can divide into a half-circle and a triangle
Half-Circle
The diameter is 6. This means that the radius is 3. Use the formula for area of a circle. Divide the answer by two since you only have a half-circle.
A = πr²
A = π(3)²
A = 9π
A = 28.274
28.274/2 = 14.137
Triangle
The base is 3 and the height 6. Use the formula for area of a triangle.
A = 1/2bh
A = 1/2(6)(3)
A = 3(3)
A = 9
Add the two areas together.
14.137 + 9 = 23.137 ≈ 23.14
The area is 23.14.
Answer:
23 sq. unitsStep-by-step explanation:
The figure consists of a semi circle and a triangle
Area of the figure = Area of semi circle + Area of triangle
Area of semi circle is 1/2πr²
where r is the radius
radius = diameter/2
radius = 6/2 = 3
Area of semi circle is
1/2π(3)²
1/2×9π
14.14 sq. units
Area of a triangle is 1/2×b×h
h is the height
b is the base
h is 6
b is 3
Area of triangle is
1/2×3×6
9 sq. units
Area of figure is
14.14 + 9
= 23.14
Which is 23 sq. units to the nearest hundredth
Hope this helps you.
an item is on sale at 40% off the regular price. it is tax at a rate of 6%. if the final sale price including tax is 50.88 then what is the sale price of the item without tax what was regular price
the sale price of the item without tax was
the regular price of the item is
Answer:
$48, $80
Step-by-step explanation:
$50.88 is the price including tax and the discount. The discount is applied first. Then the tax is applied.
The tax is 6%, so $50.88 is 106% of the discounted price.
$50.88/1.06 = $48
$48 is the discounted price.
The discount is 40% of the original price, so the pre-tax discounted price is 60% of the original price.
$48/0.6 = $80
The original price was $80
A number is tripled and then 17 is subtracted. If the
result is 40, find the original number..
Answer:
The original number is 19
Step-by-step explanation:
Let the original number be x
The above expression is written as
3x - 17 = 40
3x = 40 + 17
3x = 57
Divide both sides by 3
3x / 3 = 57/3
x = 19
Hope this helps you.
Answer:
im not sure either the triple is time with three or power of three
if times three:
3x–17=40
19
if power of three:
x³–17=40
x=
[tex] \sqrt[3]{57} [/tex]
expand the linear expression 4(10x -4)
Answer:
40x - 16
Step-by-step explanation:
(see attached for reference)
By utilizing the distributive property:
4(10x -4)
= (10x)(4) -4 (4)
= 40x - 16
Answer:
4x10x= 40x -4x4=-16 40xtimes-4<-----------thats your answer
Step-by-step explanation:
1. What line forms when a plane and a cylinder intersect?
O A. Parallel line
O B. Broken line
O C. Curved line
O D. Straight line
Answer:
A. Parallel line
Parallel line forms when a plane and a cylinder intersect
hope this helping you..
when a plane and a cylinder intersect it forms into parallel line
A.Parallel line
If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to a. 38. b. 19. c. 18. d. 39.
Answer:
Null hypothesis: [tex]\mu_1= \mu_2[/tex]
Alternative hypothesis:[tex]\mu_1 =\neq \mu_2[/tex]
And for this case we assume that we have equal variances so that means:
[tex]\sigma =\sigma_1 =\sigma_2[/tex]
For this case the degrees of freedom are given by:
[tex] df= n_1 +n_2 -2[/tex]
And replacing we got:
[tex] df= 20+20 -2= 38[/tex]
And the best answer would be:
a. 38
Step-by-step explanation:
For this problem we want to test the following:
Null hypothesis: [tex]\mu_1= \mu_2[/tex]
Alternative hypothesis:[tex]\mu_1 =\neq \mu_2[/tex]
And for this case we assume that we have equal variances so that means:
[tex]\sigma =\sigma_1 =\sigma_2[/tex]
For this case the degrees of freedom are given by:
[tex] df= n_1 +n_2 -2[/tex]
And replacing we got:
[tex] df= 20+20 -2= 38[/tex]
And the best answer would be:
a. 38
Evaluate: 26.45 + 4.79 + 120.02 - 3.20 =
Answer:
Hello There!
`~~~~~~~~~~~~~~~~~~`
26.45 + 4.79 + 120.02 - 3.20 =
148.06
Step-by-step explanation: Simplify the expression.
Hope this helped you. Brainliet would be nice!
Answer:
Step-by-step explanation:
BODMAS
Align the decimals properly
26.45 + 4.79 + 120.02 = 150.26
26.45
+ 4.79
120.02
______
151.26
______
151.26 - 3.20 = 148.06
Find the length of UC
Answer: 25 units
Step-by-step explanation:
Simply do 40(UN)-15(CN) to get 25(UC)
Hope it helps <3
Answer:
25Option D is the correct option
Solution,
Here,
UN = 40
CN = 15
Now,
UN = UC + CN
plugging the values,
40 = UC + 15
-UC = 15 - 40
-UC = -25
The difference sign (-) will be cancelled in both sides:
UC = 25
hope this helps...
Good luck on your assignment..
Can somebody please help me with this question?
Answer:
Blue Triangle.
Step-by-step explanation:
Using the area formula for a triangle, the pink triangle has an area of 0.5×54×33 in² or 891 in². The blue triangle has an area of 0.5×56×39 in² or 1092 in².
Answer:
Step-by-step explanation:
both shapes are triangles so there area is :
A=( b*h) / 2 where h is the height and b the base
triangle 1 : (pink)A= (33*54)/2 = 742.5 in²
triangle 2 : (blue)A= (56*39)/2= 1092 in²
so the blue triangle has a greather area
One movie ticket costs $7, and one small bag of popcorn costs $3. Write two equivalent expressions for the total cost of four movie tickets and four bags of popcorn. Then find the cost. a. 4($7 + $3), 4($7) + 4($3); $40 c. $4(7 + $3), $4(7) + $4($3); $12 b. 4($7 x $3), 4($7) x 4($3); $84 d. $4($7), $4($3); $28
Answer:
Option A
Step-by-step explanation:
=> 1 ticket = $7
=> 1 bag = $3
Expression # 1:
=> 4($7+$3)
Expression # 2:
=> 4($7)+4($3)
Solving it:
=> $28+$12
=> $40
Answer:
4(7+3)=28+12=40, 4(3)+4(7)
Answer: A and C
Step-by-step explanation:
For the x-values 1, 2, 3, and so on, the yvalues of a function form a geometric
sequence that decreases in value. What type of function is it?
Answer:
exponential function
Step-by-step explanation:
A geometric sequence is a representation of an exponential function.
__
There are a couple of ways an exponential function can decrease in value. It can be a decaying function, or it can be a growth function that is reflected across the x-axis.
The product of two numbers was 9. If one number is three and three fourth, what was
the other number?
Answer:
2.4
Step-by-step explanation:
3 3/4 = 3.75
9/3.75 = 2.4
a patient receives 65 grams of medicine if its increased by 20% how many grams is that
Responda:
13 gramas
Explicação passo a passo:
65 + 20% = 13
1) A grocer sold 5 kg of wheat flour at Rs 30 per kg and gained 20%. If he had sold
it at Rs 27 per kg, what would be his gain or loss percent?
Answer:
given,
selling price (sp)=rs 5 ×30
=rs 150
now, gain %=20%
cost price (cp)=
[tex] \frac{sp \times 100}{100 + gain\%} [/tex]
[tex] = \frac{150 \times 100}{100 + 20} [/tex]
therefore cp= rs125
now,
again in 2nd case
sp= rs 27×5
therefore sp=rs 135
and cp= rs125
now, sp>cp so,
[tex]gain\% = \frac{sp - cp}{cp} \times 100\%[/tex]
or, gain=
[tex] = \frac{135 - 125}{125} \times 100\%[/tex]
therefore gain %= 8%.... is answer
hope it helps..