We have to calculate a 90% confidence interval for the proportion that chose the answer "Spruce".
The sample proportion is p = 0.869:
[tex]p=\frac{X}{n}=\frac{272}{313}\approx0.869[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_p=\sqrt{\frac{p(1-p)}{n}} \\ \\ \sigma_p=\sqrt{\frac{0.869\cdot0.131}{313}} \\ \\ \sigma_p\approx\sqrt{0.0003637} \\ \sigma_p\approx0.019 \end{gathered}[/tex]The critical z-value for a 90% confidence interval is z = 1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot\sigma_p=1.645\cdot0.019\approx0.031[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=p-z\sigma_p=0.869-0.031=0.838 \\ UL=p+z\sigma_p=0.869+0.031=0.900 \end{gathered}[/tex]Answer: The 90% confidence interval for the population proportion is (0.838, 0.900).
Mrs. algebra ordered some small and medium pizzas for her daughter‘s birthday party. The small pizzas cost $5.75 each and the medium pizzas cost $8.00 each. She bought three more medium pizzas than small pizzas and her total order came to $51.50 How many pizzas of each did Mrs. Algebra order? Write an equation and solve.
we have the following:
x is small pizzas
y is medium pizzas
[tex]\begin{gathered} 5.75\cdot x+8\cdot y=51.5 \\ y=x+3 \\ 5.75\cdot x+8\cdot(x+3)=51.5 \\ 5.75x+8x+24=51.5 \\ 13.75x=51.5-24 \\ x=\frac{27.5}{13.75} \\ x=2 \end{gathered}[/tex]therefore, the answer is:
2 small pizzas and 5 (2+3) medium pizzas
What is the sum of -15 + 182A. 33B. 3c. -3 D-33Your answer
-15 + 18 is the same as 18 - 15, which is equal to 3.
help meee pleaseeee pleasee
Answer:
f(x) = (-1/4)x - 5
Step-by-step explanation:
(-8, -3), (-12, -2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -2 - (-3) -2 + 3 1 -1
m = ------------ = ------------- = ----------- = --------- = -------
x₂ - x₁ -12 - (-8) -12 + 8 -4 4
y - y₁ = m(x - x₁)
y - (-3) = (-1/4)(x - (-8)
y + 3 = (-1/4)(x + 8)
y + 3 = (-1/4)x - 2
-3 -3
-------------------------------
y = (-1/4)x - 5
I hope this helps!
1. Write the value of the digit in the hundreds place and the value of the digit in the tens place in 440. What is the relationship between the values of those two digits? The ___ in the in the hundreds place has a value _____ times as great as the____in the ____ place.
The ___ in the in the hundreds place has a value _____ times as great as the____in the ____ place.
• We have 440
,• 400 + 40
,• Four hundreds + four tens
The relationship between the values of these two digits is that they are the same, but the four in the hundreds place has a value ten times as great as the four in the tens place.
Find the solution of this system of linearequations. Separate the x- and y- values with acomma. Enclose them in a pair of parantheses. System of equations4x + 8y = 838x + 7y = 76- 8x - 16y = -1668x + 7y = 76
Given,
System of equation is,
[tex]\begin{gathered} 4x+8y=83\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
System of equation is,
[tex]\begin{gathered} -8x-16y=-166\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} -8x-16y=-166 \\ 8x+16y=166 \\ 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
1-Findes the length indicated.2- Find the angle indicated.3-Find the distance between each pair of points.
1.
LM = LN - MN
LM = 22 - 5 (Replacing)
LM= 17 (Subtracting)
2.
m∠EDW= m∠EDC - m∠WDC
m∠EDW= 106° - 40° (Replacing)
m∠EDW= 66° (Subtracting)
3.
Using the formula for the distance between two points we have:
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ x1=8,x2=-6,y1=3,y2=3 \\ d=\sqrt[]{(8-(-6))^2+(3-3)^2}\text{ (Replacing)} \\ d=\sqrt[]{(8+6)^2+(0)^2}\text{ (Subtracting)} \\ d=\sqrt[]{(14)^2^{}}\text{ (Adding)} \\ d=14\text{ (Raising 14 to the power of 2 and taking the square root)} \\ d=14 \\ \text{ The distance between these points is 14} \end{gathered}[/tex]Using the formula for the midpoint we have:
[tex]\begin{gathered} (\frac{x1+x2}{2},\frac{y1+y2}{2}) \\ x1=8,x2=-6,y1=3,y2=3 \\ (\frac{8+(-6)}{2},\frac{3+3}{2}) \\ (\frac{2}{2},\frac{6}{2})\text{ (Subtracting and adding)} \\ (1,\text{ 3) (Dividing)} \\ \text{The midpoint is (1,3)} \end{gathered}[/tex]the stock market lost 231 points on Tuesday then walks 128 more points on Wednesday find a change of points over the two days
the change of the points is:
[tex]-231-128=-359[/tex]so in the 2 days the stock market lost 359 points
H.O.T. FOCUS ON HIGHER ORDER THINKING 20. Communicate Mathematical Ideas Explain how to graph the inequality 8≥ y.
Given the inequality:
8 ≥ y
Let's graph the inequality.
To graph the inequality, take the following steps:
Step 1.
Rewrite the inequality for y and slip the inequality.
[tex]y\le8[/tex]Step 2.
Draw a solid horizontal line at y = 8.
Since the y is less than or equal to 8, shade the region below the boundary line.
Thus, we have the graph of the inequality below:
identify all pairs of alternate interior angles. Are the pairs of alternate interior angles equal in measure?
have two parallel lines L1 and L2 crosses by a secant line m.
It means that the measure of alternate interior angles is equal.
The alternate interior angles are:
∠3 and ∠6
∠4 and ∠5
a) Reflection, then translationb) Rotation, then translationc) Reflection, then rotationd) Rotation, then reflection
We have the following:
Therefore we can conclude that from step 1 to step 2, it is a rotation because it moves on its own axis and from step 2 to 3, it is a reflection
4. At a shelter, 15% of the dogs are puppies. If there are 60 dogs at the shelter, how many are puppies? * O 400 O 25 O 9 O 42
4. At a shelter, 15% of the dogs are puppies. If there are 60 dogs at the shelter, how many are puppies? * O 400 O 25 O 9 O 42
_____________________________________________________
60* (0.15) = 9
_______________________________
Answer
There are 9 puppies
a line passes through the points (2,5) and (-6,4). What is it's equation in point-slope form?
Answer:
y-5=⅛(x-2)
Explanation:
Given the points (2,5) and (-6,4).
To find the equation of the line joining these points in point-slope form, we begin by finding its slope.
[tex]\begin{gathered} \text{Slope,m}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{5-4}{2-(-6)} \\ =\frac{1}{2+6} \\ m=\frac{1}{8} \end{gathered}[/tex]Next, we substitute the slope and any of the given points into the point-slope form below:
[tex]y-y_1=m(x-x_1)[/tex]We use the point (2,5).
• x1=2, y1=5
[tex]y-5=\frac{1}{8}(x-2)[/tex]The equation in point-slope form is y-5=⅛(x-2).
Help on math question precalculus Match the description with the correct base for the logarithm.-LOG without a subscript has a base of -Ln has a base of Choices =10,e
The formal way of writing a logarithm is the following:
[tex]\log _ab[/tex]Where "a" is the base of the logarithm and "b2 is the argument.
If "a = 10", then the base is not written, like this:
[tex]\log _{10}b=\log b[/tex]In the case that the base is the constant number "e" then the logarithm is called a "natural logarithm" and it is written as follows:
[tex]\log _eb=\ln b[/tex]pls help me i’ll give ty brainlist
[tex]\sqrt{25*7x^{4}*x^{1} } \\=\sqrt{25*x^{4}*7 *x^{1} } \\=\sqrt{25x^{4} } *\sqrt{7x}\\=5x^{2} \sqrt{7x}[/tex]
Option B is the answer.
Answer: C
i hope you can see my handwriting
Thor is at the lowest point of Asgard whichis 280 feet below sea level (-280 ft.). He flies tothe highest point 520 feet above sea level(520 ft.). How far did he fly? Answer in acomplete sentence.
We have that:
We want to find how far did he fly. This means, we want to find the distance between -280 ft and 520 ft. (Which is 520 ft + 280 ft = 800 ft)
In order to find it out we substract them (we substract the first measure from the second):
520 - (-280)
Since - (-280) = +280, then
520 - (-280) = 520 + 280
= 800
Answer: he flied 800 ft
40.0 Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+95-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?
But cannot be negative, hence s= 42. This implies that 42 shirts will be sold to make a profit of exactly $2000.
To earn a profit of more than $2000, then s must be greater than 42
This makes the answer to be s > 42
The correct answer is the second option
QuestionAreli invested a principal of $950 in her bank account with an interest rate of 3%. How much interest did she earn in 5years?
$ 142.5
Explanation
to solve this we can use the formula:
[tex]i=\text{Prt}[/tex]where i is the interest, P is the principal, r is the rate ( in decimals) and t is the time
then
Step 1
Let
[tex]\begin{gathered} i=i \\ P=950 \\ r=3\text{ \% =0.03} \\ \text{Time= 5 years} \end{gathered}[/tex]replace in the formula
[tex]\begin{gathered} i=950\cdot0.03\cdot5 \\ i=142.5 \end{gathered}[/tex]hence, the answer is
$ 142.5
I hope this helps you
What’s the answer?? Just a part of a homework practice
The functions are
[tex]h(x)=0.42x^2+0.3x+4\text{ and }r(x)=-0.005x^2-0.2x+7[/tex]Multiply both functions s follows.
[tex]h(x)\times r(x)=(0.42x^2+0.3x+4)\times(-0.005x^2-0.2x+7)[/tex][tex]=0.42x^2\times(-0.005x^2-0.2x+7)+0.3x\times(-0.005x^2-0.2x+7)+4\times(-0.005x^2-0.2x+7)[/tex][tex]=0.42x^2\times(-0.005x^2)+0.42x^2\times(-0.2x)+0.42x^2\times7+0.3x\times(-0.005x^2)+0.3x\times(-0.2x)+0.3x\times7+4\times(-0.005x^2)+4\times(-0.2x)+4\times7)[/tex][tex]=-0.0021x^4-0.084x^3+2.94x^2-0.0015x^3-0.06x^2+2.1x-0.02x^2-0.8x+28[/tex][tex]=-0.0021x^4-0.084x^3-0.0015x^3+2.94x^2-0.06x^2-0.02x^2+2.1x-0.8x+28[/tex][tex]=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28[/tex]Hence the required product is
[tex]q(x)=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28[/tex]Hence the first option is correct.
HELP ASAP MATH PRE CALC
The values for the dimensions of the open box are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
The cube as a three dimensional shapes.A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices. Each face of a cube is a square. In there dimension, the cube's sides are; the L = length, W = width, and H = height.
From question, squares of equal sides x are cut out of each corner of the metal sheet, hence the dimension for the height of the box is equal to x.
So; H = (x) inches,
L = (30 - x)inches, and
W = (30 - x)inches.
Therefore, the dimensions of the box that can maximize the volume of the metal sheet of 30inches by 30inches are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
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Which equation could be represented by the number line? O A. -5 + 7 = 2 O.B. -3+(-4)= -7 O C. 4+ (-7)=-3 O D.7+(-6) = 1 SURAT E PREVIOUS
C. 4 + (-7) = -3
C. 4 + (-7) = -3 could represent by the number line because no other equation has reflected the lines' displacement of 7 grid from a certain point going to the left which is equivalent to -7.
The rest of the choices is not a possible equation to the line.
A. -5 + 7 = Displacement of 7 Grid to the Right from Point -5
B. -3 - 4 = Displacement of 4 Grid to the Left from Point -3
D. 7 - 6 = Displacement of 6 Grid to the Left from Point 7
8in 8in 8in area of irregular figures
Given data:
The given figure.
The expression for the area is,
[tex]\begin{gathered} A=(8\text{ in)(8 in)+}\frac{1}{2}(8\text{ in)( 8 in)} \\ =96in^2 \end{gathered}[/tex]Thus, the area of the given ffigure is 96 square-inches.
Please provide a deep explanation with examples so I can understand and learn, thank you
Since the package of 500 sheets has dimensions of
[tex]216\times279\times45[/tex]Since 7000 sheets will need to be put in
[tex]\frac{7000}{500}=14[/tex]14 similar package
Since the dimensions of the case are
[tex]216\times279\times270[/tex]The length and the width of the package are the same as the length and the width of the case
Then we will use the heights of them to find how many package we can put in the case
[tex]\frac{270}{45}=6[/tex]That means we can fill the case with 6 packages
Since we have 14 packages, then we will need 6 + 6 + 2
3 cases 2 full and one has 2 packages only
A food safety guideline is that the mercury in fish should be below one part per million (ppm). listed below are the amounts of mercury found in tuna sushi sampled at different stores in a major city. construct a 98% confidence interval estimate of the mean amount of mercury in the population. does it appear that there’s too much mercury in tuna sushi?0.58 0.82 0.10 0.88 1.32 0.50 0.92
The amounts of mercury found in tuna sushi sampled at different stores are:
0.58, 0.82, 0.10, 0.88, 1.32, 0.50, 0.92
Number of samples, N = 7
[tex]\begin{gathered} \text{The mean, }\mu\text{ = }\frac{0.58+0.82+0.10+0.88+1.32+0.50+0.92}{7} \\ \mu\text{ = }\frac{5.12}{7} \\ \mu\text{ =}0.73 \end{gathered}[/tex]Standard deviation
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum ^{}_{}{(x_1-\mu)^2}}{N}} \\ \sigma\text{ = }\sqrt[]{\frac{(0.58-0.73)^2+(0.82-0.73)^2+(0.10-0.73)^2+(0.88-0.73)^2+(1.32-0.73)^2+(0.50-0.73)^2+(0.92-0.73)^2}{7}} \\ \sigma\text{ =}\sqrt[]{\frac{0.9087}{7}} \\ \sigma\text{ =}\sqrt[]{0.1298} \\ \sigma\text{ = }0.36 \end{gathered}[/tex]The confidence interval is given by the equation:
[tex]\begin{gathered} CI\text{ = }\mu\pm z\frac{\sigma}{\sqrt[]{N}} \\ CI=0.73\pm2.33(\frac{0.36}{\sqrt[]{7}}) \\ CI\text{ = }0.73\pm0.32 \\ CI\text{ = (0.73-0.317})\text{ to (0.73+0.317)} \\ CI\text{ = }0.413\text{ < }\mu<1.047 \end{gathered}[/tex]Find percent change of 50 to 43
Answer:
-14.00%
Step-by-step explanation:
((43-50)/50)*100 = -14.00%
1
Pratap Puri rowed 26 miles down a river in 2 hours, but the return trip took him 6; hours. Find the rate Pratap can row
in still water and find the rate of the current. Let x=rate Pratap can row in still water and y = rate of the current.
What is the rate that Pratap rows in still water?
Pratap can row at a rate of
(Type an integer or a decimal.)
in still water.
The speed of current will be "4.5 mph" and the rate Pratap can row in still water will be "8.5 mph".
What does "speed" mean in mathematics?
Speed is what it means. the speed of a change in an object's location in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance. Speed is a scalar quantity because it just has a direction and no magnitude.Given:
Distance "26 miles" in time "2 hours".
Let,
Speed of water = y
Pratap speed when rowing in still water = x
As we know,
Speed = distance/time
then,
x + y = 26/2
x + y = 13
x = 13 - y
In return trip took him time "6.5 hours",
x - y = 26/6.5
x - y = 4
By substituting the value of "x", we get
13 - y - y = 4
13 - 2y = 4
2y = 13 - 4
2y = 9
y = 9/4 = 4.5 mph (Rate of the current)
By substituting the value of "y", we get
x = 13 - a
x = 13 - 4. 5 = 8.5 mph (Pratap can row in still water)
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a) Jayla says that the equation y=2*3 matches the graph Substitute the ordered pairs (from part() into the equation to prove that jayla is correct. Make sure to show ALL steps
From the graph let's take the points as the ordered pairs:
(3, 3), (4, 5), and (5, 7)
Given the equation:
y = 2x - 3
Let's verify for all points, if the equation matches the graph:
a) (x, y) ==> (3, 3)
Substitute 3 for x and 3 for y in the equation
y = 2x - 3
3 = 3(3) - 3
3 = 6 - 3
3 = 3
b) (x, y) ==> (4, 5)
Substitute 4 for x and 5 for y:
y = 2x - 3
5 = 2(4) - 3
5 = 8 - 3
5 = 5
c) (x, y) ==> (5, 7)
Substitute 5 for x and 7 for y:
y = 2x - 3
7 = 5(2) - 3
7 = 10 - 3
7 = 7
Since the left side equals the right side of the equation, the equation
y=2x-3 matches the graph.
Therefore, Jayla is correct.
A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
Let
x -----> number of boys
y -----> total number of children
we have that
x=11 -----> given
y=21 ----> given
therefore
The fraction of the class that is made up of boys is equal to
x/y
substitute
11/21translate the inequality into a sentence. ten subtracted from the product of 9 and a number is at most -17. use x for unknown number
in the figure shown MN is parallel to segment YZ what is the length of segment YZ
We will solve this question using the similar angle theorem
The shape consist of two triangles which i am going to draw out,
One is a big triangle while the other is a small triangle
Let NZ = a
To find NZ We will equate the ratio of the big triangle to that of the small triangle
[tex]\frac{7.5\operatorname{cm}}{3\operatorname{cm}}=\frac{(a+5)cm}{5\operatorname{cm}}[/tex]We then cross multiply to get,
[tex]\begin{gathered} 3(a+5)=7.5\times5 \\ 3a+15=37.5 \\ by\text{ collecting like terms we will have that} \\ 3a=37.5-15 \\ 3a=22.5 \\ \frac{3a}{3}=\frac{22.5}{3} \\ a=7.5\operatorname{cm} \end{gathered}[/tex]Therefore XZ=XN+NZ
[tex]XZ=5+7.5=12.5\operatorname{cm}[/tex]To calculate YZ ,
We will use the pythagorean theorem,
[tex]\begin{gathered} XZ^2=YZ^2+XY^2 \\ 12.5^2=YZ^2+7.5^2 \\ 156.25=YZ^2+56.25 \\ YZ^2=156.25-56.25 \\ YZ^2=100 \\ YZ=\sqrt[]{100} \\ \vec{YZ}=10.0cm \end{gathered}[/tex]Therefore ,
The value of YZ is
[tex]\vec{YZ}=10.0\operatorname{cm}[/tex]Hence ,
The correct answer is OPTION B
The 3D object above is sliced parallel to the base. What shape is formed? triangle octagon rectangle hexagon
When a 3D object is sliced such that the top is parallel to the base, then the top and the base formed same shape.
The shape formed at the base;
It is a six-sided shape. A six-sided polygon is called HEXAGON