Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
553 - No
70 - Not Sure
384 - Yes
Total = (553 + 70 + 384) = 1007
Proportion who do think country is headed in the right direction :
P = yes / total = 384/1007 = 0.381
b.) Error margin at 95%
Margin of Error = Zcritical * √p(1-p)/n
1-p = 1 - 0.381 = 0.619
Zcritical at 95% = 1.96
Margin of error = 1.96 * √0.381(0.619)/1007
Margin of error = 0.030
C.)
95% confidence interval for heading in the right direction:
P ± margin of error
P ± 0.030
Lower boundary = 0.381 - 0.030 = 0.351
Upper boundary = 0.381 + 0.030 = 0.411
(0.351 ; 0.411)
D.)
Confidence interval for people who don't think :
P = 553 / 1007 = 0.549
Confidence interval = P ± margin of error
Error margin at 95%
Margin of Error = Zcritical * √p(1-p)/n
1-p = 1 - 0.549 = 0.451
Zcritical at 95% = 1.96
Margin of error = 1.96 * √0.549(0.451)/1007
Margin of error = 0.031
P ± margin of error
P ± 0.031
Lower boundary = 0.549 - 0.031 = 0.518
Upper boundary = 0.549 + 0.031 = 0.580
(0.518 ; 0.580)
E.)
The interval with smaller error margin is ; 0.030 (those who think country is headed in the right direction because sample proportion is farther from .5 / farther from 1)
The length of a rectangle is four times its width.
If the area of the rectangle is 100 yd”, find its perimeter.
Answer: 50yd
Step-by-step explanation:
We know that the area of any rectangle is length times width. The perimeter is the sum of twice the length and twice the width.
Let width = x
Let length = 4x
Area = 100m2
Next, we can write an equation using these variables and formula for area.
4x2 = 100
x2 = 25
x = -5 and x = 5
Since the dimensions cannot be negative, we accept the positive value:
x = 5
Next, we can substitute this value of x into the variables.
width = 5 m
length = 20 m
Finally, we can find the perimeter by plugging in these dimensions into the perimeter formula,
Perimeter = 2(5 m) + 2(20 m)
= 10 m + 40 m
= 50 m
Raj is travelling to another country.
He flies for 5 hours at an average speed of 950 km/h on one plane.
He then flies for 6 hours 30 minutes at an average speed of 830 km/h on a second plane.
What is the total distance, in km, he travelled by plane?
Answer:
10145
Step-by-step explanation:
5 times 950 equals 4750
and 6.5 times 830 equals 5395
add first and second value
4750 + 5395 equals 10145
there is no arguing
Answer:
10145 km
Step-by-step explanation:
Time x speed = Distance
5 x 950 = 4750
6.5 x 830 = 5395
add together = 10145
Madge has cut out two triangular shapes from a block of wood, as shown below. Are the two shapes similar? Show your calculations.
the lengths of two sides of a right triangle are 12 inches and 15 inches.What is the difference between the two possible lengths of the third side of the triangle
Answer:10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
Applying the Pythagoras Theorem
Find the length of the hypotenuse
substitute
Second case
The given lengths are one leg and the hypotenuse
so
Applying the Pythagoras Theorem
Find the length of the other leg
substitute
Find the difference between the two possible lengths of the third side of the triangle
so
Answer:
The difference between the two possible lengths for the third side of the triangle is about 10.21 inches.
Step-by-step explanation:
We are given that the lengths of two sides of a right triangle is 12 inches and 15 inches.
And we want to find the difference between the two possible lengths of the third side.
In the first case, assume that neither 12 nor 15 is the hypotenuse of the triangle. Then our third side c must follow the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+(15)^2=c^2[/tex]
Solve for c:
[tex]c=\sqrt{12^2+15^2}=\sqrt{369}=\sqrt{9\cdot 41}=3\sqrt{41}[/tex]
In the second case, we will assume that one of the given lengths is the hypotenuse. Since the hypotenuse is always the longest side, the hypotenuse will be 15. Again, by the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in known values:
[tex](12)^2+b^2=(15)^2[/tex]
Solve for b:
[tex]b=\sqrt{15^2-12^2}=\sqrt{81}=9[/tex]
Therefore, the difference between the two possible lengths for the third side is:
[tex]\displaystyle \text{Difference}=(3\sqrt{41})-(9)\approx 10.21\text{ inches}[/tex]
Factor this expression completely, then place the factors in the proper location on the grid. a2b2 - d2
Answer:
[tex]{ \tt{ {a}^{2} {b}^{2} - {d}^{2} }} \\ \\ = { \tt{( {ab})^{2} - {d}^{2} }} \\ = { \tt{(ab - d)(ab + d)}}[/tex]
Find r, if 6r7 = 511 8
Answer:
121.857
Step-by-step explanation:
6×7r = 5118
42r = 5118
r = 121.857
Answer:
121.8571428571429
Step-by-step explanation:
r= 5118/42
Which of the following represents the factorization of the trinomial below?
x2 - 14x + 49
O A. (x-7)
O B. (x-7)(x+7)
O C. (x+7)
O D. (x+2)(x+7)
ANSWER ASAP!!
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: ( {x - 7})^{2} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {x}^{2} - 14x + 49[/tex]
[tex] = {x}^{2} - 7x - 7x + 49[/tex]
Taking "[tex]x[/tex]" as common from first two terms and "7" from last two terms, we have
[tex] = x \: ( \: x - 7 \: ) - 7 \: ( \: x - 7 \: )[/tex]
Taking the factor [tex](x-7)[/tex] as common,
[tex] = ( \: x - 7\:) \: (\: x - 7\: )[/tex]
[tex] =( {x - 7})^{2} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
What is an equation of the line that passes through the points (-6, 3) and (-5,2)
Answer:
y=-x-3
Step-by-step explanation:
The equation of the line passing through (2, 3) with a slope of 5 is y = [] x - []
what are the answers to []
Answer:
y = 5x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, then
y = 5x + c ← is the partial equation
To find c substitute (2, 3) into the partial equation
3 = 10 + c ⇒ c = 3 - 10 = - 7
y = 5x - 7 ← equation of line
a and b are complementary angles and a and c are supplementary angles. If a=xº, (a) express b and c in terms of x
(b) find c - b.
Step-by-step explanation:
a + b = 90
a + c = 180
a) If a = x, the. we can write
x + b = 90 and x + c = 180
or
b = 90 - x
c = 180 - x
b) c - b = (180 - x) - (90 - x)
= 180 - x - 90 + x
= 90
DJ Jacqueline is making a playlist for work; she is trying to decide what 9 songs to play and in what order they should be played. If she has her choices narrowed down to 6 jazz, 19 reggae, and 7 blues songs, and she wants to play an equal number of jazz, reggae, and blues songs, how many different playlists are possible
The following results come from two independent random samples taken of two populations.
Sample 1 Sample 2
n1 = 60 n2 = 35x1 = 13.6 x2 = 11.6σ1 = 2.1 σ2 = 3
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.
Answer:
[tex](a)\ \bar x_1 - \bar x_2 = 2.0[/tex]
[tex](b)\ CI =(1.0542,2.9458)[/tex]
[tex](c)\ CI = (0.8730,2.1270)[/tex]
Step-by-step explanation:
Given
[tex]n_1 = 60[/tex] [tex]n_2 = 35[/tex]
[tex]\bar x_1 = 13.6[/tex] [tex]\bar x_2 = 11.6[/tex]
[tex]\sigma_1 = 2.1[/tex] [tex]\sigma_2 = 3[/tex]
Solving (a): Point estimate of difference of mean
This is calculated as: [tex]\bar x_1 - \bar x_2[/tex]
[tex]\bar x_1 - \bar x_2 = 13.6 - 11.6[/tex]
[tex]\bar x_1 - \bar x_2 = 2.0[/tex]
Solving (b): 90% confidence interval
We have:
[tex]c = 90\%[/tex]
[tex]c = 0.90[/tex]
Confidence level is: [tex]1 - \alpha[/tex]
[tex]1 - \alpha = c[/tex]
[tex]1 - \alpha = 0.90[/tex]
[tex]\alpha = 0.10[/tex]
Calculate [tex]z_{\alpha/2}[/tex]
[tex]z_{\alpha/2} = z_{0.10/2}[/tex]
[tex]z_{\alpha/2} = z_{0.05}[/tex]
The z score is:
[tex]z_{\alpha/2} = z_{0.05} =1.645[/tex]
The endpoints of the confidence level is:
[tex](\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}[/tex]
[tex]2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}[/tex]
[tex]2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}[/tex]
[tex]2.0 \± 1.645 * \sqrt{0.0735+0.2571}[/tex]
[tex]2.0 \± 1.645 * \sqrt{0.3306}[/tex]
[tex]2.0 \± 0.9458[/tex]
Split
[tex](2.0 - 0.9458) \to (2.0 + 0.9458)[/tex]
[tex](1.0542) \to (2.9458)[/tex]
Hence, the 90% confidence interval is:
[tex]CI =(1.0542,2.9458)[/tex]
Solving (c): 95% confidence interval
We have:
[tex]c = 95\%[/tex]
[tex]c = 0.95[/tex]
Confidence level is: [tex]1 - \alpha[/tex]
[tex]1 - \alpha = c[/tex]
[tex]1 - \alpha = 0.95[/tex]
[tex]\alpha = 0.05[/tex]
Calculate [tex]z_{\alpha/2}[/tex]
[tex]z_{\alpha/2} = z_{0.05/2}[/tex]
[tex]z_{\alpha/2} = z_{0.025}[/tex]
The z score is:
[tex]z_{\alpha/2} = z_{0.025} =1.96[/tex]
The endpoints of the confidence level is:
[tex](\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}[/tex]
[tex]2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}[/tex]
[tex]2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}[/tex]
[tex]2.0 \± 1.96 * \sqrt{0.0735+0.2571}[/tex]
[tex]2.0 \± 1.96* \sqrt{0.3306}[/tex]
[tex]2.0 \± 1.1270[/tex]
Split
[tex](2.0 - 1.1270) \to (2.0 + 1.1270)[/tex]
[tex](0.8730) \to (2.1270)[/tex]
Hence, the 95% confidence interval is:
[tex]CI = (0.8730,2.1270)[/tex]
10 mugs and 2 plates cost £54
8 mugs and 2 plates cost £46
Write down and solve simultaneous equations
(M is the cost of a mug and p is the cost of a plate, in £
Answer:
mug = 4
plate = 7
Step-by-step explanation:
10 x + 2y =54
8x + 2y = 46
2x = 8
x = 4
2y = 14
y = 7
Of the following fractions: 9/19, 5/11, 7/15, and 11/23, which is the largest?
Answer:
silly question...I used technology to "cheat"
it is 11/23
34155 32775 33649 34485
72105 72105 72105 72105
Step-by-step explanation:
$1400 is invested at 4% per annum simple interest. How long will it take for the amount to reach $1624? Show you working.
Answer:
4 years
Step-by-step explanation:
I = prt
F = p + prt
F = 1400 + 1400 * 0.04 * t
1624 = 1400 + 1400 * 0.04 * t
224 = 56t
t = 4
Answer: 4 years
To paint interior walls, a person charges 50¢ per square foot plus the cost of the paint. For a recent job, the paint cost $100 and the total bill was $475.
The person must have painted ____ ft^2.
Answer:
750 ft²
Step-by-step explanation:
.Given :
Charge per ft² = 50¢ = $0.5
Total cost = ((charge per ft² * number of ft²) + cost of paint)
Given that :
Paint cost = $100
Total cost = $475
Number of ft² = x
Plugging values into the equation :
475 = (( 0.5 * x) + 100)
475 = 0.5x + 100
475 - 100 = 0.5x
375 = 0.5x
x = 375 / 0.5
x = 750 ft²
PLS HELPP MEE !!
Use a calculator to find the r-value of these data. Round the value to three decimal places.
The Answer is -0.985
I just took the test.
A brick staircase has a total of 17 steps The bottom step requires 131 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?
Answer: 1547 bricks are required to build the staircase.
Step-by-step explanation:
We are given:
Number of bricks in the first step, [tex]a_1[/tex] = 131
Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126
Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121
Sequence become:
131, 126, 121, .....
These are in arithmetic progression where a = 131 and d (common difference) = -5
To calculate the sum of an AP, we use the formula:
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
where,
n = number of terms = 17
Putting values in above equation, we get:
[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]
Hence, 1547 bricks are required to build the staircase.
The sum of two numbers is 12 The product of the smaller
umber and 3 is -6. Find
the numbers
Answer:
-2 and 14
Step-by-step explanation:
-2×3=-6-2+14=12The numbers are -2 and 14
What is algebraic expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11
given
Let smaller number be x and larger number be y
x * 3 = -6
x = -6/3 = -2
x+y = 12
-2 + y = 12
y = 12+2 = 14
to learn more about algebraic expression refer to:
https://brainly.com/question/4344214
#SPJ2
please help meeeeeee
pt5
Answer:
roots and zeroes.
Explanation:
Zeroes are the solution of any polynomial equation, but when it comes to quadratic equation, we use the term, roots.
So therefore, we use the term zero, for it is a polynomial, and root, for it's a quadratic equation.
Hope you understand
Thank You
Please mark as brainliest
Answer:
see explanation
Step-by-step explanation:
The solutions of a quadratic equation are referred to as
x- intercepts, roots , zeros
Which of the following phrases would represent this expression?
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3
Answer:
the quotient of x and 3
Step-by-step explanation:
x divided by 3
division answers are called quotients
Answer:
Step-by-step explanation:
x/3
• the difference of x and 3
• the quotient of 3 and x
• the product of 3 and x
• the quotient of x and 3 is correct. We are dividing x into 3, not 3 into x.
x^3y+2x^2y^2+xy^3 and 2x^3+4x^2y+2xy^2 Find the HCF.
Answer:
[tex]x(x+y)^2[/tex]
Step-by-step explanation:
We are given that
[tex]x^3y+2x^2y^2+xy^3[/tex] and [tex]2x^3+4x^2y+2xy^2[/tex]
We have to find HCF.
[tex]x^3y+2x^2y^2+xy^3=xy(x^2+2xy+y^2)[/tex]
=[tex]xy(x+y)^2[/tex]
By using the formula
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex]xy(x+y)^2=x\times y\times (x+y)^2[/tex]
[tex]2x^3+4x^2y+2xy^2=2x(x^2+2xy+y^2)[/tex]
[tex]=2x(x+y)^2[/tex]
[tex]2x(x+y)^2=2\times x\times (x+y)^2[/tex]
HCF of ([tex]x^3y+2x^2y^2+xy^3,2x^3+4x^2y+2xy^2[/tex])
[tex]=x(x+y)^2[/tex]
PLSSSS ANSWER!!!!!!!!!
Which one did you need help with?
A book store had 30816 exercise books which were paclced in cartons each carton contained 24 exercise books the mass of an empty carton was 2kg and a full carton 12kg
30,816 books would go into 1,284 containers which would weigh 15,408kg with all the books in them or 2,568kg with the books not in them.
The shoes still have a marginal cost of 25$. You want to earn a profit, so you bathe a price of what
Answer:
12
Step-by-step explanation:
Taking 0.5 cm as 1 unit, plot the following points on the graph paper: A(1,3), B (-3,-1), C (1,- 4), D (- 2,3), E (0-8), F (1.0)
Answer:
It's letter c
Step-by-step explanation:
you have to × the 0.5 and 1
find the volume of pyrmaid
Answer:
37
Step-by-step explanation:
In the given figure the angles are vertically opposite angles so ;
4x + 2 = 150
or, 4x = 148
or, x = 37 ans .
Use a net to find the surface area of the cone
to the nearest square centimeter. Use 3.14 for
20 cm
TT.
Answer:
4444
Step-by-step explanation:
Answer:
819
Step-by-step explanation:
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Plz help. I was crying. Super challenging. Will give brainiest and will give 50 points for explained answer. Thx
Answer:
Paige is incorrect. g(x) has a steeper slope
Step-by-step explanation:
The slope for f(x) is
m =( y2-y1)/(x2-x1)
= (17/2 - 5/2) / ( -1 - -6)
= (17/2 - 5/2) / ( -1 +6)
= (12/2)/5
= 6/5
The slope for g(x) is
m =( y2-y1)/(x2-x1)
= (-1 - 13/3) / ( 6 - 2)
=(-3/3 -13/3) / (6-2)
(-16/3)/4
-16/3 * 1/4
- 4/3
Comparing the magnitudes
|6/5| |-4/3|
|6/5*3/3| |-4/3*5/5|
|18/15| |20/15|
|20/15| is greater so it has a steeper slope
g(x) has a steeper slope
A custodian has 5 1/2 gallons of paint. Each of the bookcases she is painting requires 1/2 gallon of paint. How many bookcases will the custodian be able to paint with that amount of paint
A. 3
B. 4
C. 11
D. 15
