The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
How to determine the situation?The given parameters are:
Initial = 5200
Rate = 5%
Because the population by 5% every year, then the situation is a geometric sequence.
The common ratio is then calculated as:
Ratio = 1 + Rate
This gives
Ratio = 1 + 5%
Evaluate
Ratio = 1.05
Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
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The spinner of the compass is two congruent isosceles triangles connected by their bases as shown in the diagram. The base of each of these triangles is 2 centimeters and the legs are 5 centimeters.
2 congruent isosceles triangles are connected by their bases. A circle is drawn around the triangles.
If the metal used to construct the spinner costs $13.25 per square centimeter, how much will it cost to make this part of the compass? Round to the nearest cent.
Cost = $
Applying the area of a rectangle, the cost to make the part of the compass is: $129.85.
What is the Area of a Triangle?Area of a triangle = 1/2(base)(height).
Find the height of the triangle using the Pythagorean theorem:
Height = √(5² - 1²) ≈ 4.9 cm.
Base = 2 cm
Area of the two triangles = 2[1/2(base)(height)]
Area of the two triangles = 2[1/2(2)(4.9)] = 9.8 cm².
Cost to to make this part of the compass = 9.8 × $13.25 = $129.85.
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Answer: 129.82
Step-by-step explanation: its on edge I got it right :)
If the polynomials p(x) = ax³+4x²+3x-4 and q(x) = x² - 4x + a, leave the same remainder when divided by (x-3), find value of a.
Steps pls
Answer:
a = -22/13.
Step-by-step explanation:
By the Remainder Theorem
p(3) = remainder when p(x) is divided by x-3.
q(3) is equal to the same remainder.
So we have:
p(3) = q(3) , so
a(3)^3 + 4(3)^2 + 3(3) - 4 = 3^2 - 4(3) + a
27a + 36 + 9 - 4 = 9 - 12 + a
27a - a = 9 - 12 - 36 - 9 + 4
26a = -12 - 36 + 4
26a = -44
a = -44/26
a = -22/13.
A pizzeria has a choice of 15 toppings. How many ways could someone choose 3?
Select one:
a. 15
b. 455
c. 2,730
d. 3,375
Answer:
the answer is b 455
Step-by-step explanation:
15/(4×12)=455
rewrite the exponential expression to have the indi cated base.
(1/8)2*, base 2
Answer:
2^-6
Step-by-step explanation:
(1/8)^2 = (2^-3)^2 = 2^-6
URGENT, PLEASE ANSWER THESE QUESTIONS
Can send helicopter 3 but not helicopter 1 and 2.
What is distance formula?
Consider two points (x1, y1) and (x2, y2) in the two-dimension, then the distance between these two points is given by,
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
We will solve given problem as shown below:
Let fire have coordinate F (-3,-5)
Let Helicopter 1 have coordinate H1(1,4)
Let Helicopter 2 have coordinate H2(-2,3)
Let Helicopter 1 have coordinate H3(4, -2)
A. Distance between helicopter 1 and fire
[tex]=\sqrt{(1-(-3))^2+(4-(-5))^2}[/tex]
[tex]=\sqrt{16+81}[/tex]
[tex]=\sqrt{97}=9.8[/tex]
No, cannot send helicopter 1
B. Distance between helicopter 2 and fire
[tex]=\sqrt{(-3-(-2))^2+(-5-3)^2}[/tex]
[tex]=\sqrt{1+64}[/tex]
[tex]=\sqrt{65}=8.06[/tex]
No, cannot send helicopter 2
Distance between helicopter 3 and fire
[tex]=\sqrt{(4-(-3))^2+(-2-(-5))^2}[/tex]
[tex]=\sqrt{49+9}[/tex]
[tex]=\sqrt{58}=7.6[/tex]
Yes, can send helicopter 3
Hence, can send helicopter 3 but not helicopter 1 and 2.
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If you draw a card with a value of three or less from a standard deck of cards, I will pay you $208. If not, you pay me $35. (Aces are considered the highest card in the deck.) Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
The expected value of the proposition which is the net expected outcome is; $20.89.
How to find the expected value?We are given that;
There is a deck of cards.
There are 3 kinds of cards that have value under 4 (or equal). These 3 cards are 2, 3, 4 and they are in total 4 * 3 = 12 cards.
The probability that we draw such a card = 12/52 = 0.23.
Thus, the probability that we do not draw such a card = 1 - 0.23 = 0.77.
Now, If we play the game once, we will get 0.23 of the times $208 and 0.77 of the times $35.
Thus, the net total expected outcome is: (0.23*208) - (0.77*35)
= $20.89.
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Gavin collects a certain type of seashell. He has 160 seashells. The seashells' weights are distributed normally with a mean of 120 grams and a
standard deviation of 26 grams.
How many of the seashells weigh at least 68 grams?
A 109
B. 156
C. 134
D. 152
Answer:
Answer: B.156
Step-by-step explanation:
Given: Total seashells = 160
mean = 120
population standard deviation = 26 grams
The probability that the seashells weigh at least 68 grams :-'
Total seashells weigh at least 68 grams = 0.9772 x 160 = 156.352≈ 156
Hence, the correct option is B.156
please mark brainiestThere are 20 red and blue marbles in a bag. s marbles are red how many are blue?
Answer:
Step-by-step explanation:
Step-by-step explanation:
15 r blue marbles
20- 5 = 15
To model some data Gwyn ran an exponential regression and found the regression equation to be y = 6.72 x 0.996x
Answer:
y=6.72x^0.996x
Step-by-step explanation:
A 14 oz bag of flour costs $2.95 and a 28 oz bag of flour costs $6.20. What is the price per ounce of the 14 oz bag of flour?
The price per ounce of the 14 Oz bag of flour is; ¢21.1.
What is the price per ounce of the 14 oz bag of flour?Since it follows from the task content that the 14 Oz bag of flour sells for $2.95 which is equivalent to ¢295 since $1 = ¢100.
It follows that the price per ounce of the 14oz bag of flour is; = ¢295/14 = ¢21.1
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f(x) 2 square root -x^2+10 x what’s the domain
The domain of the function are all real numbers greater than 10
Domain of a functionDomain are values of the independent variables for which the function exist.
Given the function below;
[tex]f(x)=2\sqrt{-x^2+10x}[/tex]
For the function to exist, then;
-x^2+10x = 0
-x^2 = -10x
x = 10
Hence the domain of the function are all real numbers greater than 10
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In the 1980’s, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of 22,071 medical doctors participating in the study, 11,037 were randomly assigned to take aspirin and 11,034 were randomly assigned to the placebo group. Doctors in this group were given a sugar pill disguised to look like aspirin. After six months, the proportion of heart attacks in the two groups was compared. Only 104 doctors who took aspirin had a heart attack, whereas 189 who received the placebo had a heart attack. Can we conclude from this study that taking aspirin reduced the chance of having a heart attack? the purpose of this study was to determine whether taking an aspirin daily reduces the proportion of heart attacks.
There is enough evidence to conclude that taking aspirin cannot reduces the chance of cancer.
Given sample size of patients take aspirin 11037, sample size of patients who have assigned placebo group be 11034. 104 doctors who take aspirin had a heart attack, 189 doctors had placebo had heart attacks.
First we have to form hypothesis.
[tex]H_{0} :p{1} -p_{2} =0[/tex]
[tex]H_{1}:p_{1} -p_{2} < 0[/tex]
We have to find the respective probabilities.
[tex]p_{1}[/tex]=104/11037
=0.0094
[tex]p_{2}[/tex]=189/11034
=0.0171
Now their respective margin of errors.
[tex]s_{1}[/tex]=[tex]\sqrt{ {(0.0094*0.9906)/11037}[/tex]
=0.0009
[tex]s_{2}[/tex]=[tex]\sqrt{0.0171*0.9829}[/tex]
=0.0011
Hence the distribution of the differences,they are given by:
p=[tex]p_{1} -p_{2}[/tex]
=0.0094-0.0171
=-0.0077
S=[tex]\sqrt{s_{1} ^{2}+s_{2} ^{2} }[/tex]
=[tex]\sqrt{(0.0009)^{2} +(0.0011)^{2} }[/tex]
=0.00305
z=(p -f)/S (In which f=0 is the value tested at the null hypothesis)
=(-0.0077-0)/0.00305
=-2.52
p value will be 0.005.
p value of 0.05 significance level.
z=1.96.
1.96>0.005
So we will reject the null hypothesis which means it cannot reduce the whole chance of becomming a heart attack.
Hence there is enough evidence to conclude that taking aspirin cannot reduces the chance of cancer.
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The graph of f(x) = 1/3
is reflected vertically, compressed horizontally by a factor of 5, shifted
right 2 units and down 6 units. Write the equation of the new graph.
The transformed function is defined by:
g(x) = -f(x/5 - 2) - 6
Where f(x) is the given function.
How to get the equation of the transformed function?Here we start with the function:
f(x) = (1/3)*x
(I don't know if this is the actual function, but that does not matter, I will solve it in a general way).
If first, we reflect it vertically, then the new function is:
g(x) = -f(x).
If now we compress it horizontally by a factor of 5, then we get:
g(x) = - f(x/5)
Now we shift it 2 units to the right, then:
g(x) = -f(x/5 - 2)
Finally, we shift it down 6 units, then we get:
g(x) = -f(x/5 - 2) - 6
That is the general form of the function g(x).
Replacing f(x) by what is defined above, we get:
g(x) = -(1/3)*(x/5 - 2) - 6
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In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$
The measure of angle D in the convex pentagon ABCDE is 132°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the measure of angle D, hence:
angle A = x - 40.
∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angle in a pentagon)
3(x - 40) + 2x = 540
x = 132°
The measure of angle D in the convex pentagon ABCDE is 132°
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A rectangular paperboard measuring 20 invhes long and 15 inches wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.)
The perimeter of the rectangle is 70 Inches square
How to determine the perimeterThe formula for perimeter of a rectangle is given as;
Perimeter = 2 ( l + w)
length = 20 inches
width = 15 inches
Perimeter = 2 ( 20 + 15 )
Perimeter = 2 ( 35)
Perimeter = 70 Inches square
Thus, the perimeter of the rectangle is 70 Inches square
Note that it is a general knowledge on the given question.
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(X+m)(c+n) if m=5 and n=-7
Answer: -7/5
Step-by-step explanation:
x = - 5cm^2 - 7m^2 + 35/ m (5c - 7), C = (cross out the equal sign) 7/5 and m = (cross out the equal sign) 0 and n = -7/5
What is the correct mathematical equation: the monthly consumption ,w, of a household is 237 litres per day with an additional monthly free water usage of 1200 litres. the household spends l litres per month is?
The linear equation for the cost that the household spend in water is given by:
C(d) = 237d + 1200.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the free usage of 1200 liters is the y-intercept, while the daily usage of 237 liters is slope. Hence the function for the amount the household spends in water in d days is given as follows:
C(d) = 237d + 1200.
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Which sequence of transformations produces A’B’C’ from ABC?
On a coordinate plane, triangle A B C has points (3, negative 1), (4, negative 4), (1, negative 2). Triangle A prime B prime C prime has points (negative 2, 3), (1, 4), (negative 1, 1).
a translation up 3 and then a 90º counterclockwise rotation about the origin
a 90º counterclockwise rotation about the origin and then a translation up 3
a reflection over the x-axis and then a translation left 2 and down 1
a translation left 5 and down 2 and then a reflection over the x-axis
Answer:
The first chose is correct
Step-by-step explanation:
You can see in the first picture that graphed both of the triangles and then I followed the directions. It is very, very helpful if you have tracing paper. You can trace the original and then translate it three up. For the 90 rotation, put a small + on the origin of your tracing paper, then move the tracing paper one one turn on the plus sign. That would be 90 degrees.
Find the measures of the numbered angles in each rhombus.
Answer:
Step-by-step explanation:
2=27
3=27
5=27
1=126
4=126
Given: ΔABC is a right triangle and CD ⊥ AB.
Prove: AC2 + BC2 = AB2
Which reason completes the proof?
A.
Corresponding sides of similar triangles are proportional.
B.
Corresponding parts of congruent triangles are congruent.
C.
Corresponding parts of similar triangles are congruent.
D.
Corresponding sides of congruent triangles are proportional.
Answer:
Corresponding parts of similar triangles are congruent.
Step-by-step explanation:
A new car is purchased for $45, 000 and over time its value depreciates by one half
every 3.5 years. What is the value of the car 17 years after it was purchased, to the
nearest hundred dollars?
Joel spends 272727 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of 606060 minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?
Joel spent 72.5% of his time exercising after playing soccer on Tuesda
How to determine the percentage?The given parameters are
Minutes spent on Tuesday = 27 more minutes than Monday
Total minutes spend = 60
This means that
Tuesday = Monday + 27
Monday + Tuesday = 60
Make Monday the subject in Tuesday = Monday + 27
Monday = Tuesday - 27
Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60
Tuesday - 27 + Tuesday = 60
Evaluate
2 * Tuesday = 87
Divide by 2
Tuesday = 43.5
The percentage of time spent exercising on Tuesday is then calculated as
Percentage = 43.5/60 * 100%
Evaluate the expression
Percentage = 72.5%
Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday
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The ratio of the number of galleons to the number of galleys in the spanish armada is 5 : 1 . what missing information could be used to find the total number of galleons to galleys in the spanish armada ?
The amount of the galleys or the number of galleys.
If given the amount of galleons, you can find the amount of galleys by dividing the number of given galleons by 5.
If given the amount of galleys, you can find the amount of galleons by multiplying the number of given galleys by 5.
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find the value of k.
(x^2+5x+k)/(x+6) has a remainder of 9.
if anyone could help, please do!! this is urgent!
The value of k in the polynomial is 3
How to solve for k?The quotient is given as:
(x^2+5x+k)/(x+6)
The remainder is 9
Set the denominator to 0
x + 6 = 0
Solve for x
x = -6
This means that:
f(-6) = 9
So, we have:
(-6)^2 + 5(-6) + k = 9
Evaluate
6+ k = 9
Subtract 6 from both sides
k = 3
hence, the value of k is 3
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Y is inversely proportional to the square of x. If Y = 2 when x = 8, then Y = , when x is_______.
The value of x when y =2 is 8
How to solve for x?The inverse proportion to the square of x represented as:
k = yx^2
Where
k represents the constant of proportion
When y = 2, x = 8.
So, we have:
k =2 * 8^2
k =128
Substitute k = 128 in k = yx^2
So, we have:
yx^2 = 128
When y = 2, we have:
2x^2 = 128
Divide by 2
x^2 = 64
Take the square roots
x = 8
Hence, the value of x when y =2 is 8
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hi can you please help me
Answer:
See attached image
Step-by-step explanation:
I'm uncertain as to the "best statement." None seem to accurately describe the situation. I picked the one that was least incorrect (if that makes any sense).
pls help :,)
What is the area of this triangle?
units²
Answer:
6 [tex]units^{2}[/tex]
Step-by-step explanation:
The formula for the area of a triangle is A = [tex]\frac{1}{2} bh[/tex]. The base in this case is the length of DE, 4 - 1 = 3 units. The height of this triangle is 1 + 3 = 4 units.
A = [tex]\frac{1}{2} bh[/tex] = [tex]\frac{1}{2} *3*4[/tex] = 6
can someone please help me
Each of the following is an example of quantitative data, except Group of answer choices weight in ounces income in dollars political affiliation age in years
The correct option is C. political affiliation.
An example of quantitative data are-
weight in ouncesage in yearsincome in dollarsWhat is quantitative data?Data that expresses a definite quantity, amount, or range is known as quantitative data. In most cases, the data is accompanied with measuring units, such as metres in the case of a person's height. Setting boundaries for such data makes sense, and performing mathematical operations on the data has significance.
Types of Quantitative Data are-
Counter: A measure of entities. For instance, the quantity of users who have downloaded a specific app from the App Store.Measurement of physical objects: Calculating the dimensions of any physical object is called measurement. The HR executive, for instance, meticulously measures the size of each cubicle given to the new hires.Sensory calculation: Mechanism to automatically "sense" the parameters being monitored in order to generate a continuous source of data. A digital camera, for instance, transforms electromagnetic signals into a string of numerical data.Data projection: Algorithms and other mathematical analysis techniques can be used to project future data. For instance, after conducting a thorough investigation, a marketer will forecast a rise in sales following the introduction of a new product.To know more about quantitative data, here
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The complete question is-
8. Each of the following is an example of quantitative data, except ______.
A. weight in ounces
B. income in dollars
C. political affiliation
D. age in years
The counting numbers beginning with 101 and ending with 200 are listed. How many of the numbers have a 6 as a digit
Counting numbers from 101 to 200, those with 6 as a digit are 19
The numbers
Let's start by listing all the number between 101 and 200
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Now, let's count the numbers with 6 as a digit
= 19 numbers has 6 as a digit
Thus, counting numbers from 101 to 200, those with 6 as a digit are 19
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