Bias can be reduced by taking a larger sample is false because an increase in sample tends to reduce the sampling error but a large sample size cannot correct for the methodological problems (undercover, nonresponse bias, etc.) that produce survey bias.
How do I solve these problems ? I'm suppose to write the first five terms of each sequence
ANSWER
a1 = -6
a2 = 30
a3 = -150
a4 = 750
a5 = 3750
EXPLANATION
The first 5 terms are a1, a2, a3, a4 and a5. To find them we just have to replace n by the number of term 2, 3, 4, or 5. For the first term we don't have to do this because it's already given:
[tex]a_2=-5a_1=-5\cdot(-6)=30[/tex][tex]a_3=-5a_2=-5\cdot30=-150[/tex][tex]a_4=-5a_3=-5\cdot(-150)=750[/tex][tex]a_5=-5a_4=-5\cdot750=3750[/tex]1 and the probability that event A occurs given 7 In an experiment, the probability that event B occurs is 9 2 that event B occurs is 7 What is the probability that events A and B both occur? Simplify any fractions.
Given :
The probability of B = 7/9
And the probability of A given B = 2/7
we need to find the probability of A and B So, it will be as follows:
[tex]P(A\cap B)=P(B)\cdot P(A|B)[/tex]so, the answer will be:
[tex]\frac{7}{9}\cdot\frac{2}{7}=\frac{2}{9}[/tex]so, the answer will be 2/9
I have 12 coins in my pocket. They are all either dimes or nickels. The value of the coins is .85 how many of each coin do I have
To solve this problem, we will set and solve a system of equations.
Let x be the number of nickels you have in your pocket, and y the number of dimes, then with the given information, we can set the following system of equations:
[tex]\begin{gathered} 0.05x+0.10y=0.85, \\ x+y=12. \end{gathered}[/tex]Multiplying the second equation by -0.10 and adding it to the first equation, we get:
[tex]0.05x-0.10x+0.10y-0.10y=0.85-1.2.[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} -0.05x=-0.35, \\ x=\frac{-0.35}{-0.05}, \\ x=7. \end{gathered}[/tex]Solving the second equation of the system for y, we get:
[tex]y=12-x.[/tex]Finally, substituting x=7, we get:
[tex]y=12-7=5.[/tex]Answer: [tex]\begin{gathered} 7\text{ nickels, } \\ 5\text{ dimes.} \end{gathered}[/tex]AThe number that is used to multiply thevariable is called the coefficient. In thisexpression, what is the coefficient?2 + 4yBC4y2PH
Answer:
4
Step-by-step explanation:
Since the number that is used to multiply the variable is called the coefficient, identify the number that goes with the variable ''y'', in this case, it is 4.
Your pet groomer charges according to how much your dog weighs. For a dog that weighs 20 pounds or less, the groomer charges $25. For a dog that weighs more than 20 pounds and less than 50 pounds, the groomer charges $45. For any dog that weighs 50 pounds or more, the groomer charges $45 plus an additional $1 for each pound over 50. Using this situation, match each piece of the piecewise function with the corresponding domain restriction.
Explanation
Given: The pet groomer charges according to the dog weights as follows:
[tex]\begin{gathered} If\text{ }weight\leqslant20,then\text{ }charge=\text{ \$}25 \\ \\ If\text{ }weight\text{ }is\text{ }between\text{ }20\text{ }and\text{ }50,then\text{ }charge=\text{ \$}45 \\ \\ If\text{ }weight\geqslant50,then\text{ }charge=\text{ \$}45+\text{ \$}1\text{ }for\text{ }each\text{ }pound\text{ }over\text{ }50 \end{gathered}[/tex]Required: To match each piece of the piecewise function with the corresponding restriction.
This is achieved thus:
==> For the first function
[tex]\begin{gathered} f(x)=25 \\ \\ \text{ This function satisfies the condition for x is greater than zero but less than or equal to 20} \end{gathered}[/tex]==> For the second function
[tex]\begin{gathered} f(x)=45 \\ \\ \text{ This function satisfies the condition for x is greater than 20 but less than 50.} \end{gathered}[/tex]==> For the third function
[tex]\begin{gathered} f(x)=45+1(x-50) \\ \\ \text{ This function satisfies the condition for x is greater than or equal to 50} \end{gathered}[/tex]Hence, the answers are:
f(x) = 25 ==> 0 less than x less than or equal to 20
f(x) = 45 ==> 20 less than x less than 50
f(x) = 45 + 1(x - 50) ==> x greater than or equal to 50.
I’m having a difficult time figuring this out. Can you please help me?
The Solution.
The equation of the line is given by the formula below:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope of the line, given as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Picking 2 points in the line, we have
[tex](-2,2)\text{ and (4,6)}[/tex]That is,
[tex]\begin{gathered} (x_1=-2,y_1=2) \\ (x_2=4,y_2=6) \end{gathered}[/tex]So, finding the slope,m, we have
[tex]m=\frac{6-2}{4--2}=\frac{4}{4+2}=\frac{4}{6}=\frac{2}{3}[/tex]So, substituting into the formula for the equation of a line, we get
[tex]y-2=\frac{2}{3}(x--2)[/tex][tex]y-2=\frac{2}{3}(x+2)[/tex]Cross multiplying, we get
[tex]3(y-2)=2(x+2)[/tex][tex]3y-6=2x+4[/tex][tex]3y-2x=4+6[/tex][tex]3y-2x=10[/tex][tex]or\text{ 3y=2x+10}[/tex]Therefore, the correct answer is 3y = 2x + 10 or 3y - 2x = 10
A child's toy soap bubble wand creates approximately spherical bubbles. The surface area of a soap bubble varies directly as the square of the radius of the bubble. If a bubble with a radius of 3 inches has a surface area of 113 square inches, what is the surface area (in square inches) of a bubble that has a radius of 4 inches? Round to the nearest tenth of a square inch. (See Example 2 in this section.)_______ in2
Given:
The surface area of a soap bubble varies directly as the square of the radius of the bubble.
Let the surface area = A
Let the radius = r
so,
[tex]\begin{gathered} A\propto r^2 \\ A=k\cdot r^2 \end{gathered}[/tex]where: (k) is the constant of proportionality
If a bubble with a radius of 3 inches has a surface area of 113 square inches
so,
When r = 3 inches, A = 113 square inches
Substitute with (r) and (A) to find the value of (k)
[tex]\begin{gathered} 113=k\cdot3^2 \\ 113=9k \\ k=\frac{113}{9} \end{gathered}[/tex]so, the equation will be:
[tex]A=(\frac{113}{9})r^2[/tex]we will find the surface area when the radius = 4 inches
So, when r = 4 inches
[tex]A=(\frac{113}{9})\cdot4^2=\frac{113}{9}\cdot16=200.8889[/tex]Rounding to the nearest tenth
So, the answer will be: the surface area = 200.9 square inches
The distance that a spring will stretch varies directly as the force applied to the spring. A force of 80 pounds is needed to stretch a spring 8 inches. what force is required to stretch the spring 18 inches?
The equation that describes the stretching of springs is:
[tex]F=k\cdot\Delta x\text{.}[/tex]Where F is the force applied to stretch the spring a length Δx and k is the constant of the spring.
In this case, we have:
[tex]\begin{gathered} F_1=80pd,\text{ }\Delta x_1=8in, \\ F_2=?,\text{ }\Delta x_2=18in\text{.} \end{gathered}[/tex]Replacing the values of F_1 and Δx_1 in the equation above, we have:
[tex]\begin{gathered} F_1=k\cdot\Delta x_1, \\ 80pd=k\cdot8in\text{.} \end{gathered}[/tex]Solving for k, we get:
[tex]k=\frac{80pd}{8in}=10\frac{pd}{in}.[/tex]Replacing the value of k and Δx_2 in the equation, we get the value of F_2:
[tex]F_2=k\cdot\Delta x_2=10\frac{pd}{in}\cdot18in=180pd\text{.}[/tex]Answer
The force required to stretch the spring 18 in is 180 pounds.
Hello I need help the the bonus question I am not sure if this is a monthly loan or a compound interest problem
Given:
Amount = $12,500
Loan A = 6% annually for 5 years
Loan B = 5.34% annually for 6 years.
Let's find the loan deal which is better.
To find the better loan deal, we have:
• Loan A:
Apply the formula:
[tex]undefined[/tex]Say 400 is 100%, what would 236 be as a percentage lower than 100%
Macy is returning from her school. She travels 2 miles west and 3 miles north. How far is she from her school?
Draw a diagram to show Macy's movements:
Notice that a right triangle is formed, where the hypotenuse has the same length as the distance from Macy to the School. According to the Pythagorean Theorem, the hypotenuse has a length which is the square root of the sum of the squares of the legs of the right triangle:
[tex]\begin{gathered} d=\sqrt[]{(3)^2+(2)^2} \\ =\sqrt[]{9+4} \\ =\sqrt[]{13} \\ \approx3.61 \end{gathered}[/tex]Therefore, she is approximately 3.61 miles apart from the school.
Determine the length of x in the triangle. Give your answer to two decimal places.
SOLUTION:
Step 1:
In this question, we are meant to determine the length of x in the triangle.
We are also expected to give your answer to two decimal places, using the diagram below:
Step 2;
Using Pythagoras' theorem, we have that:
[tex]\sin 20^0=\text{ }\frac{12}{x}[/tex]Making x, the subject of the formulae, we have that:
[tex]x\text{ = }\frac{12}{\sin 20^0}[/tex][tex]x\text{ =}\frac{12}{0.3420}[/tex][tex]\begin{gathered} x\text{ = 35. 0877193} \\ x\text{ }\approx\text{ 35. 09 ( two decimal places)} \end{gathered}[/tex]CONCLUSION:
The length of x in the triangle = 35. 09 ( two decimal places)
Write x <-6 or x>6 as an absolute value inequality.
|x| >6
1) Let's write x < -6 or x > 6 as an absolute value inequality
So, we can write
|x| > 6 Applying the Absolute value property
x > 6
|x| > 6 Applying the Absolute value property
x < -6
SO the answer is |x| >6
Find the greatest common factor of these two expressions.12x^5u^8 and 18w^2x^4u^6
Answer:
Explanations
Given the following terms
[tex]12x^5u^8and18w^2x^4u^6[/tex]Find the factors of each term
[tex]\begin{gathered} 12x^5u^8=6\cdot2\cdot x^4\cdot x\cdot u^6\cdot u^2 \\ 18w^2x^4u^6=6\cdot3\cdot w^2\cdot x^4\cdot u^6 \end{gathered}[/tex]Next is to get the common factors from both terms. From the factors derived, we can see that the common factors are 6 * x^4 * u^6
Hence the greatest common factor of these two expressions is 6x^4
the value of the polynomial when y equals -3 The polynomial is 5y - 11y² + 13
Answer
The value of the polynomial when y = -3 is
-101
Explanation
The polynomial is given as
5y - 11y² + 13
We are then asked to find the value when y = -3
5y - 11y² + 13
= 5(-3) - 11(-3)² + 13
= -15 - 11 (9) + 13
= -15 - 99 + 13
= -101
Hope this Helps!!!
What is the answer to 187x+(-8x)
Let's simplify the expression, first we cancel the parenthesis:
187x+-(8x), ten:
since a plus sign multiplied by a minus sign gives us a minus sign we have:
187x-8x
now, we just substract 8 to 187, since both numbers are multiplied by the same variable (x)
then:
(187-8)x=179x
and that's it
187x+(-8x)=179x
I need help on answering number problems 14 and 15.
Given the vertices of a polygon
W: (5, -1)
X: (5,6)
Y: (2,-1)
Z: (2,6)
We will graph the polygon on a grid of x-y plane
the graph will be as shown in the following picture:
As shown, the polygon is a rectangle:
Length = the distance between (5,-1) and (5,6) = 7 units
Width = the distance between (5,6) and (2,6) = 3 units
The perimeter = 2*(length + width) = 2 * (7+3) = 2 * 10 = 20
Area = Length x width = 7 x 3 = 21
So, the answer will be:
Perimeter = 20 units
Area = 21 square units
How can the surface area of the onion be approximated?The surface area of the onion can best be modeled by a . Based on the model, the approximate surface area of the onion is square inches.
Answer:
[tex]\text{ SA=38.5 square inches}[/tex]Step-by-step explanation:
As we can see the onion seems like a sphere, therefore we can use the equation for the surface area of a sphere, which is represented by the following equation;
[tex]SA=4\pi *r^2[/tex]estimating the radio of the onion, r=1.75. The estimated surface area would be:
[tex]\begin{gathered} \text{ SA=4\lparen3.14\rparen}*1.75^2 \\ \text{ SA=38.5 square inches} \end{gathered}[/tex]Find each product 8.5 x 4
The answer is very simple. .
The product is
[tex]\begin{gathered} 8.5\cdot\text{ 4 = }34\text{ } \\ 8.5\cdot \\ 4\text{ } \\ \end{gathered}[/tex]34.0 is the answer
i got to classify if its a acute or obtuse or right and justify my answer
The triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side. The square of the longest side is less than the sum of the squares of two smaller sides.
So here,
[tex]\begin{gathered} 8.6^2=73.96 \\ 5.3^2=28.09 \\ 3.2^2=10.24 \\ 10.24+28.09=38.33 \end{gathered}[/tex]Therefore, we have,
[tex]3.2^2+5.3^2<8.6^2[/tex].Thus, the triangle is obtuse.
in diagram ABC the measure of ABC which type of transformation is shown
Notice that the distance from each vertex A, B and C to the Y axis is the same as the distance from the Y axis to their corresponding images A'. B' and C'.
Then, the transformation that was performed to ABC was a reflection over the Y axis. Then, the answer is:
[tex]\text{ Reflection}[/tex]Use the place values of 35 to fill in the blanks in parentheses.Then, give the value of 2 x 35.(a) 2 x 35 = (2 x D)- (DХа 6?(b) 2 x 35
In 35, 3 is in the tens place and 5 is in the ones place, that is,
place value of 3: 30
place value of 5: 5
This means that 35 can be expressed as 30 + 5.
Substituting 35 = 30 + 5 into the multiplication given, we get:
[tex]\begin{gathered} 2\cdot35=2\cdot(30+5) \\ \text{Distributing the multiplication over the addition:} \\ 2\cdot35=(2\cdot30)+(2\cdot5) \\ \text{ Solving each multiplication on the right} \\ 2\cdot35=60+10 \\ 2\cdot35=70 \end{gathered}[/tex]
If H is the midpoint of GI, find GH.5x+2 9x - 10H
GH=17
1) Since GI is the midpoint then, it is fair to say that
GH is congruent to HI
So, 5x +2 =9x-10
5x+2-9x=9x-9x-10
-4x+2=-10
-4x+2-2=-10-2
-4x=-12
x=3
2) The question wants GH
Let's plug x =3
5(3) +2
15+2
17
GH=17
Need help with what numbers you subtract or how to solve for this chart
Solution
Given the score selected at random from an exam score at Math course:
75 62 80 40 91
[tex]mean=\frac{75+62+80+40+91}{5}=\frac{348}{5}=69.6[/tex]Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Solve each equation.x2=144
Solving the equation:
[tex]x^2=144[/tex]Procedure:
0. Getting the square root of both sides.
[tex]\sqrt[]{x^2}=\sqrt[]{144}[/tex]2. Simplifying:
[tex]x=12[/tex]Answer: x = 12
Emma rode 8 times as fast as Emily . In fact , she rode 48 kilometers in 4 hours less than it took Emily to ride 36 miles . How fast did each of them ride ? How long did they ride ?
Let M be Emma's speed and E be Emily's speed. Since Emma rode 8 times as fast as Emily, we can write it as
[tex]M=8\times E[/tex]Now, we know that she rode 48 km in 4 hours less than it took Emily to ride 36 miles. This means that
[tex]\begin{gathered} \\ \\ 48km=M\times(t-4hours) \end{gathered}[/tex]and
[tex]36\text{miles}=E\times(t)[/tex]where t denotes the time in which they rode the same distance.
From the second equation,we have
[tex]\begin{gathered} \\ (t-4)=\frac{48}{M}\ldots(A) \end{gathered}[/tex]and for the third equation, we have
[tex]\begin{gathered} \\ t=\frac{36}{E}= \end{gathered}[/tex]Now, we need to convert units, from miles to kilometers. We know that 1miles is equal to 1.6km, then we get
[tex]\begin{gathered} \\ 36\text{miles}=36\text{miles(}\frac{1.6\operatorname{km}}{1mile})=57.6\text{ km} \end{gathered}[/tex]then, our last equation is equivalent to
[tex]t=\frac{57.6}{E}\ldots(B)[/tex]By substituting equation B into equation A, we have
[tex]\frac{57.6}{E}-4=\frac{48}{M}\ldots(C)[/tex]Then, we have 2 equations in 2 unknows, that is, our first equation and equation C. Then, By substituting our first equation into equation C, we have
[tex]\begin{gathered} \frac{57.6}{E}-4=\frac{48}{8\cdot E} \\ or \\ \frac{57.6}{E}-4=\frac{6}{E} \end{gathered}[/tex]By moving the right hand side to the left hand side and -4 to the right hand side, we have
[tex]\frac{1}{E}(57.6-6)=4[/tex]which gives
[tex]\begin{gathered} \\ \frac{51.6}{E}=4 \\ E=\frac{51.6}{4} \\ E=12.9(\frac{\operatorname{km}}{hour}) \end{gathered}[/tex]with this result, we can find M by substituting this values into our first equation, that is,
[tex]\begin{gathered} M=8\times E \\ M=8\times12.9 \\ M=103.2(\frac{\operatorname{km}}{hour}) \end{gathered}[/tex]Then, for the first question How fast did each of them ride ? The answer is
[tex]\begin{gathered} \text{Emma's sp}eed=103.2\text{ }\frac{\operatorname{km}}{hour} \\ \text{Emily's sp}eed=12.9\text{ }\frac{\operatorname{km}}{hour} \\ \end{gathered}[/tex]Now, in order to find how long they ride, we need to find the time t. We can find it by substituting E into equation B, that is
[tex]\begin{gathered} t=\frac{57.6}{E} \\ t=\frac{57.6}{12.9} \\ t=4.46\text{ hour} \end{gathered}[/tex]Then, the distance is
[tex]103.2(\frac{km}{\text{hour}})(4.46\text{hour)}=460.8\text{ km}[/tex]then, How long did they ride ? 460.8 kilometers
A pancake recipe ask for 2 2/3 times as much milk as flour. if 4 1/3 cups of milk is used what quantity of flour would then be needed according to the recipe
Given:
Quantity of milk used = 4⅓ cups
The recipe asks for 2⅔ times as much milk as flour.
Let's find the amount of floor that would then be needed according to the recipe.
To find the quantity of floor needed, we have:
[tex]F=4\frac{1}{3}\div2\frac{2}{3}[/tex]Convert the mixed fractions to improper fractions:
[tex]F=\frac{13}{3}\div\frac{8}{3}[/tex]Change the division sign to mutiplication and flip the fraction on the right:
[tex]F=\frac{13}{3}\ast\frac{3}{8}=\frac{13}{8}=1\frac{5}{8}[/tex]Therefore, the quantity of flour that would be needed according to the recipe is 1⅝ cups.
ANSWER:
[tex]1\frac{5}{8}\text{ cups of floor}[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is greater than or equal to 4". Find P(A). Outcome Probability 1 0.08 2 0.06 3 0.35 4 0.14 5 0.09 6 0.14 7 0.14
From our table, we can note that the probability of the event A="greater or equal than 4" will be given by
[tex]P(\text{A)=P(4)+P(5)+P(6)+P(7)}[/tex]which gives
[tex]\begin{gathered} P(A\text{)=0.14+}0.09+0.14+0.14 \\ P(A\text{)=}0.51 \end{gathered}[/tex]therefore, the probability of the event A is equal to 0.51.
I need help finding the measure of angle are you to the nearest hundred
Given data:
The first side given is a =100 ft.
The second side is b=249 ft.
The expression for tan(A) is,
[tex]\begin{gathered} \tan (A)=\frac{a}{b} \\ \tan (A)=\frac{100\text{ ft}}{249\text{ ft}} \\ A=\tan ^{-1}(\frac{100}{249}) \\ =21.88^{\circ} \\ \approx22^{\circ} \end{gathered}[/tex]Thus, the angle A is 22 degrees, so second option is correct.
As you move the slider for supplemental angles, what do you notice about the sum of the two angles?Draw two of the supplemental angles you made using the demonstration. How would you know when twoangles are supplemental? What would be a good definition for supplemental angles?
A good definition for supplemental angles is that they are adjacent angles which sum 180°. In other words, they form a straight angle.
If we have supplemental angles and we move the central line that divides the angles, the total sum will be still 180° because they are supplementary.
So, we can conclude that two supplementary angles always sum 180°, no matter if one angle is 10° and the other 170°, they will always be on a straight angle which sums 180°.
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