Final answer:
To find the length of the child's shadow, set up a proportion comparing the woman's height and shadow length to the child's height and unknown shadow length. Solving the proportion 64/40 = 58/Child's shadow, we find that the child's shadow is approximately 36.25 inches long.
Explanation:
The question involves using proportions to calculate the length of the child’s shadow. Since the child is shorter than the woman, we can expect that the child’s shadow will also be shorter in proportion to her height. The woman is 5 feet and 4 inches tall, which converts to 64 inches. The shadow to height ratio is the same for both individuals because they are standing under the same lighting conditions.
We can set up a proportion using the woman’s height and shadow length to find the child’s shadow length:
Woman’s height / Woman’s shadow = Child’s height / Child’s shadow
64 inches / 40 inches = 58 inches / Child’s shadow
To solve for the child’s shadow, we cross-multiply:
64 * Child’s shadow = 58 * 40
Child’s shadow = (58 * 40) / 64
Child’s shadow = 2320 / 64
Child’s shadow = 36.25 inches
Therefore, the child’s shadow is roughly 36.25 inches long.
Researchers at the National Cancer Institute re- leased the results of a study that investigated the effect of weed-killing herbicides on house pets. They examined 827 dogs from homes where an herbicide was used on a regular basis, diagnosing malignant lymphoma in 473 of them. Of the 130 dogs from homes where no herbicides were used, only 19 were found to have lymphoma.a) What’s the standard error of the difference in the two proportions? b) Construct a 95% confidence interval for this difference. c) State an appropriate conclusion.
Answer:
A)The Standard error for difference in proportion is 0.0354
B)The Confidence interval with 95 % for difference in proportion is (0.356 ,0.495)
C)The conclusion is that proportion of herbicides and no herbicides and having them diagnosed with malignant lymphoma is between 35.6 % and 49.5 % And higher than the proportion to pets in homes where no pesticides were used.
Step-by-step explanation:
Given:
Total dogs which are herbicide =827=n1
diagnosing malignant lymphoma Dogs=473
Total no herbicides Dogs=130=n2
19 were found to have lymphoma.
To Find:
a)What’s the standard error of the difference in the two proportions?
b) Construct a 95% confidence interval for this difference.
c) State an appropriate conclusion
Solution:
The standard error of difference is given by ,
Consider S1 for case 1 (herbicides) and S2 for case 2 (no herbicides)
So
[tex]S1-S2=Sqrt[p1(1-p1)/n1 +p2(1-P2)/n2)][/tex]
Here[tex]p1=473/827[/tex] =0.578 and [tex]p2=19/130[/tex]=0.146
[tex]S1-S2=Sqrt[0.572(0.428)/827 +0.146(0.854)/130][/tex]
[tex]S1-S2=Sqrt[2.96e-4 +9.59e-4][/tex]
[tex]S1-S2=Sqrt[0.001255][/tex]
[tex]S1-S2=0.0354[/tex]
This gives the difference between two proportions 0.0354
Now,
For 95 % C.I it is given by for above difference at Z=1.96
[tex]C.I.=[p1-p2-Z*Sqrt[p1(1-p1)/n1 +p2(1-P2)/n2) ,p1-p2+Z*Sqrt[p1(1-p1)/n1 +p2(1-P2)/n2)][/tex]
[tex]C.I=0.426-1.96*Sqrt[0.57(0.42)/827 +0.146(0.85)/130],0.426+1.96*Sqrt[0.57(0.42)/827 +0.146(0.85)/130][/tex]
[tex]C.I.=(0.356,0.495)[/tex]
The conclusion is that proportion of herbicides and no herbicides and having them diagnosed with malignant lymphoma is between 35.6 % and 49.5 % And higher than the proportion to pets in homes where no pesticides were used.
Y/8=5 y= ? Please help me
Answer: y Y/40 should be your answer
Answer:
Y=40
Step-by-step explanation:
40/8=5
Functions of the form y = abx, where b > 0 and b ≠ 0, are called ____ functions.
Answer:
Exponential function.
Step-by-step explanation:
We are given that a function of the form
[tex]y=ab^x[/tex]
Where [tex]b\neq 0[/tex] and b>0
Exponential function: The function is of the form
[tex]y=b^x[/tex]
Where b is a positive constant and greater than 0 and x is any real number.
The given function satisfied the define of exponential function.
Hence, the function of the form [tex]y=ab^x[/tex]
Where b>0 and [tex]b\neq 0[/tex] are called exponential function.
Functions of the form y = ab^x, where b > 0 and b ≠ 0, are called Exponential Functions. They are widely used in mathematical and scientific contexts.
Explanation:
Functions of the form y = abx, where b > 0 and b ≠ 0, are called Exponential Functions. These functions represent a wide range of phenomenons in mathematics and natural science. An exponential function represents a quantity which is increasing or decreasing at a rate proportional to the magnitude of the quantity itself. For example, a savings account with an interest rate of 2% would exhibit exponential growth since the magnitude of the account balance would increase at a rate proportional to the balance itself.
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Maya is building a sandbox that is 40 inches wide. The length of the sandbox is four times the width of the sandbox. What is the perimeter of the sandbox?
Answer:400 is the perimeter
Step-by-step explanation:
Answer:
200 inches
Step-by-step explanation:
40*4=160
160+40=200
(-3, 5) is located in _____.
A.Quadrant I
B.Quadrant II
C.Quadrant III
D.Quadrant IV
Mr.Meyer draws a shape on the board.It has 4 sides of equal length and 4 right angles.List all of the names possible to describe the shape Mr.Meyer drew.
Answer:
The Quadrilateral namely as
1)Square .
2)Rhombus.
Step-by-step explanation:
Given :
Four sides and 4 angels are equal
To find :
Which quadrilateral are possible?
Solution:
We know that 4 sides are equal and 4 right angles are of square
And It ,s properties are acquired by the shape Rhombus
with equal sides and opposite side are parallel to each other and angles are of right angle (90 degrees).
And many Quadrilaterals have right angle but not 4 equal sides
(Pic of rhombus is shown below)
The population of Smalltown in the year 1890 was 6,250. Since then, it has increased at a rate of 3.75% each year. • What was the population of Smalltown in the year 1915? • In 1940? • What will the population of Smalltown be in the year 2003? • When will the population reach 1,000,000 (to the nearest year)?
Answer:
year 1915 : 15,689year 1940 : 39,381t = 137.9 years
Step-by-step explanation:
Hi, to answer this question we have to apply an exponential growth function:
A = P (1 + r) t
Where:
p = original population
r = growing rate (decimal form)
t= years
A = population after t years
Replacing with the values given:
A = 6,250 (1 + 3.75/100)^t
A = 6,250 (1 + 0.0375)^t
A = 6,250 (1.0375)^t
So, by the year 1915 :1915-1890 = 25 years passed (t)
A = 6,250 (1.0375)^25
A = 15,689
by the year 1940 :1940-1890 = 50 years passed (t)
A = 6,250 (1.0375)^50
A = 39,381
When will the population reach 1,000,000?. We have to subtitute A=1000000 and solve for t.1,000,000= 6,250 (1.0375)^t
1,000,000/ 6,250 =(1.0375)^t
160 = 1.0375^t
log 160 = log 1.0375^t
log 160 = (t ) log 1.0375
log160 / log 1.0375= t
t = 137.9 years
Using the compound interest formula to model population growth, the population of Smalltown in the years 1915, 1940, and 2003 is calculated to be approximately 13,194, 33,605, and 459,383 respectively. The population is projected to reach 1,000,000 in the year 2032.
Explanation:To solve this problem, we use the formula for compound interest, which is also used for population growth, it is P(1 + r)^n where P is the initial amount (or population in this case), r is the rate of increase and n is the number of years.
For the population in 1915, we subtract 1890 from 1915 to get 25 years. The formula becomes: 6250(1 + 0.0375)^25. Using a calculator, this gives us approximately 13,194.For the population in 1940, we subtract 1890 from 1940 to get 50 years. The formula thus becomes: 6250(1 + 0.0375)^50. Using a calculator, this gives us approximately 33,605.For the population in 2003, we subtract 1890 from 2003 to get 113 years. The formula becomes: 6250(1 + 0.0375)^113. This gives us approximately 459,383.To find out when the population of Smalltown will reach 1,000,000, we rearrange our formula to solve for n (the number of years). That gives us n = log([1,000,000/6250]) / log(1 + 0.0375). Using a calculator, we find that n is approximately 142 years, so the year would be 1890 + 142 = 2032.Learn more about population growth here:
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what is the area of a triangle with 11 1/2 height and 14ft base
Answer:
80.5 feet
Step-by-step explanation:
The formula for a triangle is 1/2 base times height. So it is 1/2 of 14 times 11 1/2. Which is also equal to 7 times 11 1/2. That equals 80.5. I hope this helps! Please mark me brainliest!
Three coins are tossed in the air, one at a time. What is the probability that the third coin will be heads?
Answer:
1/2
Step-by-step explanation:
We only care about the third coin
we could get heads or tails on the third flip
P (third coin will be heads) = outcome heads / total
=1/2
Answer:
½
Step-by-step explanation:
Trials are independent
If the coin is unbiased,
P(T) = P(H) = ½ for every trial
how many numbers have an absolute value of 6
Answer:
2
Step-by-step explanation:
Final answer:
The numbers that have an absolute value of 6 are -6 and 6.
Explanation:
An absolute value represents the distance between a number and zero on a number line. It is always a positive value. In this case, we are looking for numbers with an absolute value of 6. To find these numbers, we need to find all numbers that are 6 units away from zero.
The numbers that have an absolute value of 6 are: -6 and 6. These two numbers are equidistant from zero, with a distance of 6 units in either direction.
So, there are two numbers with an absolute value of 6.
Using Trig to find angles !! help please
56.1°.
Step 1 The two sides we know are Opposite (300) and Adjacent (400).
Step 2 SOHCAHTOA tells us we must use Tangent.
Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
Step 4 Find the angle from your calculator using tan-1
What is SOH CAH TOA?"SOHCAHTOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent, (1) (2).
Please check the attached file for a brief answer.
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I need major help I know it’s not 2, 1, and .25 for sure please help
Answer:
a = 9
b = 3
c = 1
Step-by-step explanation:
hope it helps
Name a polygon that would have a
sum of Its Interior angles larger than
7201 degrees and less than 7500
degrees.
Answer:
The polygon has 43 sides . The polygon can be called 43 - gon or tetracontakaitrigon.
Step-by-step explanation:
In a regular polygon all the sides are equal and also all the angles are equal. The sum of the interior angle of a polygon can be calculated with the following formula;
sum of interior angle = (n−2) × 180°
where
n = number of sides
The sum of the interior angle should be less than 7500 and greater than 7201.
sum of interior angle = (n−2) × 180°
less than 7500 and greater than 7201 = (43 - 2) × 180
less than 7500 and greater than 7201 = 41 × 180
less than 7500 and greater than 7201 = 7380 °
The polygon has 43 sides . The polygon can be called 43 - gon or tetracontakaitrigon.
The graph shows the high temperatures on july 4th over a 15 year period. What is the approximate probability that next year’s temperature (year 16) will be in the 90s?
Answer:
it’s 0.53
Step-by-step explanation:
wigger fart
To calculate the probability of the temperature being in the 90s next year, you take the number of times the temperature was in the 90s over the past 15 years and divide by 15. This gives the probability, but it is just an estimate as weather is unpredictable.
Explanation:To determine the probability that next year’s temperature will be in the 90s, you firstly need to know the number of times the temperature was in the 90s over the past 15 years. After that, you divide that by the total number of years observed (15 years). This gives a fraction or a decimal which represents the probability.
For instance, if the temperature was in the 90s for 7 out of the 15 years, the probability would be 7/15, or approximately 0.47.
Please remember, this result is an estimate as weather is influenced by many unpredictable factors. Therefore, the past trends cannot guarantee future conditions but it gives a rough estimate.
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What's the definition of statistics?
Answer:
statistics is defined as:
the branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.
Final answer:
Statistics is a mathematical discipline focused on data collection, analysis, interpretation, and presentation. It includes both the process of dealing with numerical data and the resulting numerical facts used to make decisions. The field consists of descriptive statistics and statistical inference, which help understand and compare data for informed decision-making.
Explanation:
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of numerical data. It encompasses the entire process from gathering the data to drawing conclusions based on the numerical information obtained. Statistics can also refer to the numerical facts themselves, which are derived from these processes. The field is divided into two key areas: descriptive statistics, which summarizes data from a sample using indexes such as mean or standard deviation, and statistical inference, which makes predictions about a population based on a sample of data.
Statistics are not confined to mere numbers; they represent a comparison and understanding of numerical data. These comparisons help us make informed decisions in various fields, from public policy to medicine. For example, statistics can tell us the percentage increase in a population over a decade, enabling policymakers to plan resources accordingly. Statistics is integral to our daily lives, even though many may not realize its pervasive influence.
The lemgth of a rectangle is 4 more than 2 times its width. Find the lemgth and width of the rectangle with an area of 160. What is the length and width?
Answer:
The length of the rectangle = 20
The width of the rectangle = 8
Step-by-step explanation:
Step(l):-
let 'W' be the width of the rectangle
Given the length of a rectangle is 4 more than 2 times its width
length of a rectangle(L) = 4+2W
Given the Area of rectangle = 160
Step(ii):-
we know that the area of the triangle = length ×width
(4+2w)w= 160
[tex]2w^{2} +4w-160=0[/tex]
[tex]2(w^{2} +2w- 80)=0[/tex]
[tex]w^{2} +10w-8w- 80=0[/tex]
[tex]w(w +10)-8(w+10)=0[/tex]
[tex](w+10)(w-8) =0[/tex]
[tex]w+10=0 , w-8=0[/tex]
w = -10 and w =8
Step(lll)
we can choose the width is 'w' = 8
now the length of the rectangle = 4+2(8) = 20
The width of the rectangle is '8'
Conclusion:-
The length of the rectangle = 20
The width of the rectangle = 8
What are the x-intercepts of the following problem?
f(x) = (x - 2)(- 3)
Jack’s mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Answer:
16 friends
Step-by-step explanation:
If the question you're asking is how many friends he gave chocolates to, the answer would be 16.
50 - 2 = 48 (You subtract 2 because it's the amount of chocolates he had left)
48 ÷ 3 = 16 (Now you divide 48 by the number of chocolates he was giving his
friends. The final answer is the amount of times he gave out
chocolates, a.k.a how many friends he has
What is the volume of the pyramid?
12StartRoot 3 EndRoot cm3
16StartRoot 3 EndRoot cm3
24StartRoot 3 EndRoot cm3
32StartRoot 3 EndRoot cm3
Answer:
[tex]16\sqrt{3}[/tex] [tex]cm^{3}[/tex]
Step-by-step explanation:
I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo,
A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4StartRoot 3 EndRoot cm and an area of 12StartRoot 3 EndRoot cm2.
What is the volume of the pyramid?
My answer:
As we know, The volume of a pyramid = [tex]\frac{1}{3}[/tex]base area × its height
Given:
Side lenght of the base is; [tex]4\sqrt{3} cm[/tex]=> The area of the base is [tex]12\sqrt{3}[/tex] [tex]cm^{2}[/tex]
In Δ ACB measure of angle ACB is 90° and m∠ CAB is 30°We use: [tex]tan(30) = \frac{BC}{AC}[/tex]
<=> BC = [tex]4\sqrt{3}*tan(30)[/tex]
= 4 cm
And BC is the height of the the pyramid
=> The volume of a pyramid = [tex]\frac{1}{3}[/tex] [tex]12\sqrt{3}[/tex] [tex]cm^{2}[/tex] * 4 cm
= [tex]16\sqrt{3}[/tex] [tex]cm^{3}[/tex]
please help!! urgent
Answer:
D, 342 meters
Step-by-step explanation:
We can use the definition of sines to solve the problem. Remember, sine = opposite leg over the hypotenuse of the triangle.
[tex]sin(<Q)= \frac{RS}{QR} \\[/tex]
Then, we can substitute QR for 1,000 and [tex]<Q[/tex] for 20 degrees and solve like so:
[tex]sin(20) = \frac{RS}{1,000}[/tex]
[tex]RS = 1000 (sin(20))\\\ RS = 1000(0.342)\\\\RS= 342.0201[/tex]
Rounding that number, we get 342 meters. Hope this made sense!
Answer: D. 342 m
Step-by-step explanation:
The given triangle is a right angle triangle since angle S is 90°.
From the given right angle triangle,
QR represents the hypotenuse of the right angle triangle.
With m∠Q as the reference angle,
QS represents the adjacent side of the right angle triangle.
RS represents the opposite side of the right angle triangle.
To determine RS, we would apply
the Sine trigonometric ratio.
Sin θ, = opposite side/hypotenuse. Therefore,
Sin 20 = RS/1000
RS = 1000Sin20 = 1000 × 0.342
RS = 342 m
URGENT: how many cubes with side lengths of 1/3 cm does it take to fill the prism
Answer:
48 cubes
Step-by-step explanation:
The total area of the cubes would be 1/27. Because 1/3*1/3*1/3=1/27.
The area of the prism is 16/9.
2 2/3 x 2/3=16/9
16/9 * 1 = 16/9
Because we want to find a common denominator we would multiply 16/9 by 3 to get 48/27.
Last, we take 48/27 and divide that by 1/27.
48/27 divided by 1/27 = 1296/27 = 48
Answer:
48 have a good day
Step-by-step explanation:
Can you guys please help me out
Answer:about 54%
Step-by-step explanation:
The weights of packages of crackers are normally distributed with a mean of 340 grams and a standard deviation of 12 grams.
What is the weight of a package of crackers with a z-score of −1.4 ?
Enter your answer in the box.
Answer: the weight of the package of crackers is 323.2 grams
Step-by-step explanation:
Since the weights of packages of crackers are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = weights of packages of crackers.
µ = mean weight
σ = standard deviation
From the information given,
µ = 340 grams
σ = 12 grams
The z score of the package is - 1.4
Therefore,
- 1.4 = (x - 340)/12
Cross multiplying by 12, it becomes
- 1.4 × 12 = x - 340
- 16.8 = x - 340
x = - 16.8 + 340
x = 323.2 grams
The circle below has a center H. Suppose that m FG=42. Find the following.
The measure of angle FHG = 42 degrees. This is the same as the arc length.
The measure of angle FEG = 21 degrees. This is half the value of the arc length.
The measure of angles are
[tex]m < FHG= 42\\m < FEG= 21 \\[/tex]
Central angle :Central angle is equal to intercepted arc.
Also, inscribed angle is equal to half of the intercepted arc.
From the given diagram ,
Central angle is angle FHG.
Given that measure of Arc FG = 42 degrees
Central angle = intercepted arc
Central angle is same as intercepted arc.
[tex]m < FHG= m (arc FG)\\m < FHG= 42[/tex]
Inscribed angle is equal to half of the intercepted arc.
To find inscribed angle , we divide the intercepted arc by 2.
[tex]m < FEG=\frac{1}{2} (arc FG)\\m < FEG=\frac{1}{2} (42)\\m < FEG= 21[/tex]
The following angles are
[tex]m < FHG= 42\\m < FEG= 21 \\[/tex]
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What is the approximate difference in tenths between
10 and
15?
sqrt 10 = 3.16
sqrt 15 = 3.87
So the difference would be 0.7
Answer:
0.7
Step-by-step explanation:
7 critics liked the sequel to My Giant. This represents 10% of all critics. How many
critics reviewed it in all?
Answer: 70 critics
Step-by-step explanation: if 7 critics is 10% of all critics, and if 7 x 10 is 70, then there where 70 critics in total
70 critics reviewed the sequel of My Giant.
The number of critics who reviewed the sequel to My Giant can be calculated using the information given.
7 critics represent 10% of all critics. Let's denote the total number of critics as 'x'.
10% of x = 7 critics.
0.10x = 7
Solving for x, x = 70.
Help please!
Image Attached
Answer:
97.92m
Step-by-step explanation:
132.65-34.73=97.92
It should be the answer
Sorry if its wrong
Alyssa is an ecologist who studies the change in the fox population of the Arctic circle over time. She observed that the population loses \dfrac{1}{18} 18 1 start fraction, 1, divided by, 18, end fraction of its size every 222 months. The population of foxes can be modeled by a function, PPP, which depends on the amount of time, ttt (in months). When Alyssa began the study, she observed that there were 185{,}000185,000185, comma, 000 foxes in the Arctic circle. Write a function that models the population of the foxes ttt months since the beginning of Alyssa's study.
To model the population of foxes t months since the beginning of Alyssa's study, we can use the equation P(t) = P(0) - (1/18t), where P(0) is the initial population of 185,000 foxes.
Explanation:To write a function that models the population of foxes t months since the beginning of Alyssa's study, we need to determine the rate at which the population decreases over time. Given that the population loses 1/18 of its size every 22 months, we can use this information to develop an equation. Let P(t) represent the population of foxes at time t, and let P(0) be the initial population of 185,000 foxes.
Since the population loses 1/18 of its size every 22 months, the rate of decrease can be calculated as 1/18 per 22 months. This can be written as -1/18 per month or -1/18t per month. Hence, the equation that models the population is P(t) = P(0) - (1/18t).
Which formula gives the x-coordinates of the maximum values for y = cos(x)?
k(pi) for any integer k
k(pi) for k= 0, +/-2, +/-4...
k(pi)/2 for any positive integer k
k(pi)/2 for k= k= 0, +/-2, +/-4...
Answer:
the correct answer is B i got it right on my test
Step-by-step explanation:
Answer:
The answer is B) k(pi) for k= 0, +/-2, +/-4,...
Step-by-step explanation:
edg
Problem 1
3x + y = –14
-2x-y=9
Answer:
x = -5 , y = 1
Step-by-step explanation:
Solve the following system:
{3 x + y = -14 | (equation 1)
-2 x - y = 9 | (equation 2)
Add 2/3 × (equation 1) to equation 2:
{3 x + y = -14 | (equation 1)
0 x - y/3 = (-1)/3 | (equation 2)
Multiply equation 2 by -3:
{3 x + y = -14 | (equation 1)
0 x+y = 1 | (equation 2)
Subtract equation 2 from equation 1:
{3 x+0 y = -15 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by 3:
{x+0 y = -5 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = -5 , y = 1