Answer:
ln [2^4 * 5^3]
Step-by-step explanation:
Rewrite 4 ln 2 as ln 2^4 and 3 ln 5 as ln 5^3.
Then 4 In 2+3 In 5 = ln 2^4 + ln 5^3, which in turn becomes
ln [2^4 * 5^3]
Suppose the correlation between height and weight for adults is 0.80. What proportion (or percent) of the variability in weight can be explained by the relationship with height
Answer: 64% of the variability in weight can be explained by the relationship with height.
Step-by-step explanation:
In statistics, Correlation coefficient is denoted by 'r' is a measure of the strength of the relationship between two variables.Coefficient of determination, [tex]r^2[/tex], is a measure of variability in one variable can be explained variation in the other.Here, r= 0.80
[tex]\Rightarrow\ r^2= (0.80)^2=0.64[/tex]
That means 64% of the variability in weight can be explained by the relationship with height.
The variability in weight is 64 % , explained by the relationship with height.
Correlation coefficients are always values between -1 and 1, where -1 shows a perfect, linear negative correlation, and 1 shows a perfect, linear positive correlation.
The correlation coefficient is measure the strength of the linear relationship between two variables in a correlation analysis.
Correlation coefficient is represented by r.
Given that, the correlation between height and weight for adults is 0.80.
[tex]r=0.8[/tex]
The variability in weight is, = [tex]r^{2}=(0.8)^{2} =0.64[/tex]
Thus, the variability in weight is 64 % , explained by the relationship with height.
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What is the scale factor of ABC to DEF?
Answer:
B.3
Step-by-step explanation:
to get the scale factor divide a side from the bigger triangle by the equivalent in the small one
15/5 = 3
see attached the question is in an image attached
37.62202 sq units
First, calculate the areas of the separate triangles:
ABD = 20.19968 sq units
ACD = 17.46234 sq units
then add them to get 37.62202 sq units
Answer:
30.51 units^2
Step-by-step explanation:
Well to find the area of a triangle without height we use the following formula,
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]
To find S we use the following formula,
[tex]S = \frac{1}{2} (a+b+c)[/tex]
So a b and c are the sides of a triangle, we'll start with the left triangle.
S = 1/2(7 + 5.22 + 7.4)
S = 1/2(19.62)
S = 9.81
Now we can plug in 9.81 for S,
[tex]A = \sqrt{9.81(9.81-a)(9.81-b)(9.81-c)}[/tex]
[tex]A = \sqrt{9.81(9.81-7)(9.81-5.22)(9.81-7.4)}[/tex]
[tex]A = \sqrt{9.81(2.81)(4.59)(2.41)}[/tex]
[tex]A = \sqrt{9.81(31.083939)}[/tex]
[tex]A = \sqrt{304.93344159}[/tex]
[tex]A = 17.46234353086664[/tex]
But we can just simplify that to the nearest hundredth place which is,
17.46.
Now for the next triangle,
[tex]S = \frac{1}{2} (6.36 + 6.85 + 7.4)[/tex]
[tex]S = \frac{1}{2} (20.61)[/tex]
[tex]S = 10.305[/tex]
Plug in 10.305 for S,
[tex]A = \sqrt{10.305(10.305-6.36)(10.305-6.85)(10.305-7.4)}[/tex]
[tex]A = \sqrt{10.305(3.945)(3.455)(2.905)}[/tex]
[tex]A = \sqrt{10.305(16.534975)}[/tex]
[tex]A = \sqrt{170.392917375}[/tex]
A = 13.053463807549
We can round it to the nearest hundredth,
A = 13.05
So we just add 17.46 + 13.05
= 30.51 units^2
Thus,
the area of the figure is 30.51 units^2.
Hope this helps :)
Which graph shows the solution to the equation below? log Subscript 3 Baseline (x + 3) = log Subscript 0.3 (x minus 1)
Answer:
The answer is 20
Step-by-step explanation:
(Edge2020)
Answer:
Its A on edge
Step-by-step explanation:
i took the test. good luck guys!
show all work!! Plus this is the same question as my last one so you get a total of 25 points if you answer both! Just copy the answer you got from this one and paste it in the other question (the same question)
Answer:
increase of 30
Step-by-step explanation:
1255- 1075 = 180
This is an increase of 180
Divide by the number of numbers which is 6
180 /6 = 30
The mean will increase by 30
Answer:
+30
Step-by-step explanation:
1255- 1075 = 180
180 /6 = 30
Brainliest for the correct awnser!!! Which of the following is the product of the rational expressions shown below?
Answer:
[tex] \frac{ {x}^{2} - 1 }{ {x}^{2} - 25 } [/tex]Step-by-step explanation:
[tex] \frac{x - 1}{x + 5} \times \frac{x + 1}{x - 5} [/tex]
To multiply the fraction, multiply the numerators and denominators separately
[tex] \frac{(x - 1) \times (x + 1)}{(x + 5) \times (x - 5)} [/tex]
Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] simplify the product
[tex] = \frac{ {x}^{2} - 1 }{ {x}^{2} - 25 } [/tex]
Hope this helps..
Best regards!!
When a survey was conducted among 100 students to find their favorite pizza topping, 45 students voted for pepperoni, 25 for mushrooms, and 30 voted for cheese. If a pie chart were made showing the number of votes for each topping, the central angle for the cheese sector would be __________.
Answer:
The central angle for the cheese sector would be 108 degrees.
Step-by-step explanation:
We know that a pi chart takes the form of a circle so the total angle measure is 360 degrees.
Now we want to find out what ratio of the pie chart that cheese takes up and apply it to the total degree measure.
30 of 100 students voted for cheese:
so the ratio would be 30/100 or 3/10
Now apply that to the total angle measure:
3/10*360 degrees= 108 degrees.
Tessellations that use more than one one type of regular polygon are called regular tessellations?
Answer:
False
Step-by-step explanation:
A tessellation refest to a shape that is repeated over and over again covering a plane without any gaps or overlaps. The statement is false given that regular tessellations use only one polygon. Semi-regular tessellations are created with more than one type of regular polygon.
−x<−29 solve for x answer must me simplified
Answer:
x > 29
Step-by-step explanation:
−x<−29
Divide each side by -1, remembering to flip the inequality
x > 29
Answer:
x > 29 → x ∈ (29; ∞)Step-by-step explanation:
-x < -29 change the signs
x > 29
Using the quadratic formula y=4x ²-81
Answer:
[tex]\huge\boxed{x=\pm4.5}[/tex]
Step-by-step explanation:
The quadratic formula of
[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
[tex]y=4x^2-81\to 4x^2-81=0\\\\a=4;\ b=0;\ c=-81[/tex]
substitute
[tex]x=\dfrac{-0\pm\sqrt{0^2-4(4)(-81)}}{2(4)}=\dfrac{\pm\sqrt{1296}}{8}=\dfrac{\pm36}{8}=\pm4.5[/tex]
A 25-foot ladder is placed against a building and the top of the ladder makes a 32° angle with the building. How many feet away from the building is the base of the ladder?
Answer:
since the top of the ladder is making the angle, the of the ladder's base from the building is our opposite and the ladder is the hypotnuse,
sin (32)=opp/hyp, 0.52=opp/25, opp=13 ft
Marking BRAINLIEST :D easy radical functions
Answer:
[tex]\large \boxed{\sf \ \ \ -4x^2+8x-8 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex](f-g)(x)=f(x)-g(x)\\\\=3x-1 - (4x^2-5x+7)\\\\=3x-1-4x^2+5x-7\\\\=-4x^2+8x-8[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A heating pad takes 3,030 Watts during each time it is turned on. If you only use it for 34 minutes, how much CO2 was created? Round to 1 decimal.
Answer:
1.7kW/hrStep-by-step explanation:
Using the formula for calculating the energy used up during the process;
Energy used up = Amount of CO₂ created.
Energy used up in the process = Power * Time.
Given Parameters:
Power = 3,030Watts
Converting to Kilowatts, power = 3030/1000 kW
Power (in kW) = 3.03kW
Time taken = 34 minutes
Converting to hour;
Since 60 minutes = 1hr
34minutes = (34/60)hr
34minutes = (17/30)hr
Required:
Energy used up = 3.03 * 17/30
Energy used up = 51.51/30
Energy used up = 1.717 kW/hr
Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.
A toy falls from a window 70 feet above the ground. How long does it take the toy to hit the ground?
Answer:
2.09 seconds.
Step-by-step explanation:
We are given...
y = 70 feet
v0 = 0 feet/second
a = 32 feet/second^2
We need to find t using the following equation...
y = v0 * t + (1/2) * a * t^2
70 = 0 * t + (1/2) * 32 * t^2
70 = (1/2) * 32 * t^2
70 = 16t^2
16t^2 = 70
t^2 = 4.375
t = sqrt(4.375)
t = 2.091650066
So, it will take the toy about 2.09 seconds to hit the ground.
Hope this helps!
Assume the weight of Valencia oranges is normally distributed with a mean 9 oz and standard deviation 2 oz. What is the probability that a sample of 100 units show a mean weight of less than 9.5 oz?
Answer:
0.99379
Step-by-step explanation:
The first thing to do here is to calculate the z-score
mathematically;
z-score = x-mean/SD/√(n)
From the question x = 9.5 ,
mean = 9, SD = 2 and n = 100
Plugging the values we have;
z-score = (9.5-9)/2/√(100) = 0.5/2/10 = 0.5/0.2 = 2.5
So the probability we want to calculate is;
P(z<2.5)
We use the standard table for this
and that equals 0.99379
Find a formula for an for the arithmetic sequence.
Answer:
[tex]a_{n} = a + 2(n-1)[/tex]
Step-by-step explanation:
[tex]a_{5}= a_{1} + 4d \\4 = -4 +4d\\8= 4d\\d= 2\\\\Therefore \\a_{n} = a_{1} + 2(n-1)[/tex]
The mean of normally distributed test scores is 82 and the standard deviation is 5. If there are 241 test scores in the data sample, how many of them were in the 92 to 97 range?
Answer:
5
Step-by-step explanation:
Find the z-scores.
z = (x − μ) / σ
z₁ = (92 − 82) / 5
z₁ = 2
z₁ = (97 − 82) / 5
z₂ = 3
Find the probability:
P(92 < X < 97)
P(2 < Z < 3)
P(Z < 3) − P(Z < 2)
0.9987 − 0.9772
0.0215
Find the number of tests:
0.0215 (241) ≈ 5
Which one doesn’t belong? Why? Explain.
Answer:
(x - 2)(x + 2)
Step-by-step explanation:
(x - 2)(x + 2) = x² - (2)² [Since (a - b)(a + b) = a² - b²]
= x² - 4
There are two terms in this expression. Therefore, the give term is a binomial.
(2x - 1)(x + 4) = 2x(x + 4) - 1(x + 4) [Distributive property]
= 2x² + 8x - x - 4
= 2x² + 7x - 4
There are three terms in this polynomial. Therefore, the given polynomial is a trinomial.
(x + 4)(x + 1) = x(x + 1) + 4(x + 1)
= x² + x + 4x + 4
= x² + 5x + 4
This polynomial is having 3 terms therefore, it's a trinomial.
(m - 4)(m + 1) = m(m + 1) - 4(m + 1)
= m² + m - 4m - 4
= m² - 3m - 4
Therefore, this polynomial is a trinomial.
Since (x - 2)(x + 2) is a binomial, so this expression doesn't belong to this group.
Lines $y=(3a+2)x-2$ and $2y=(a-4)x+2$ are parallel. What is the value of $a$?
Answer:
-8/5Step-by-step explanation:
Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same
Let's get the slope of both equation. For the first equation;
y=(3a+2)x-2
We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2
Similarly for the second line;
2y=(a-4)x+2
Re-writing in the standard format we will have;
y = (a-4)x/2+2/2
y = (a-4)x/2 + 1
The slope of the second line is (a-4)/2
On equating the slope of both lines to get the value of 'a' we will have;
3a+2 = (a-4)/2
Cross multiplying
2(3a+2) = a-4
6a+4 = a-4
Collecting like terms;
6a-a = -4-4
5a = -8
a = -8/5
Hence the value of a is -8/5
A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius,
Each of the central angles has a measure of 40' How many sides does the polygon have?
8
9
010
O 12
Answer:
9 sides
Step-by-step explanation:
The formula for number of sides of a polygon with a given central angle
Number of sides = 360°/ central angle
In the above question, we were told that each of the central angles in the polygon ha a measure of 40°
Hence,
Number of sides = 360°/40°
9 sides.
Therefore, the number of sides that polygon in the above question has is 9 sides.
Find the approximate sum of the series shown below.
Answer:
its D
Step-by-step explanation:
The approximate sum is 134.83
The correct option is (D).
What is series?
A series in math is simply the sum of the various numbers or elements of the sequence.
For example, to make a series from the sequence of the first five positive integers 1, 2, 3, 4, 5 we will simply add them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.
A series in math is the sum of the terms in a sequence. The series and the sequence given in this example are almost identical. What differentiates the two is the addition of the + sign. Changing the comma to a plus sign changes the sequence into a series.
Suppose a person wanted to increase their level of fitness. The person decides to walk for 15 minutes the first day and increases the time spent walking by 5 minutes each day for the first week. The sequence that shows this example is
15, 20, 25, 30, 35, 40, 45
series used to find the answer is
15+20+25+30+35+40+45
Given:
[tex]\sum[/tex] (k =1 to 8) 5* (4/3)^(k-1)
So,
Putting values k=1 to 8 one by one then
= 5 + 20/3 + 80/9+0320/27+......+81920/2187
=294875/2187
=134.83
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43.
Some of the ingredients used by a baker for making 1 dozen
normal sponge cakes are listed below:
225g unsalted butter; 4 eggs; 125ml milk;
2 tsp vanilla extract; 264g plain flour
To make fully vegetarian cakes, the baker replaces each egg
with an additional 30g of plain flour.
The baker got an order for 100 normal cakes and 60 vegetarian
cakes. How much kilograms of flour would the baker need to
complete the order?
Answer:
4.12 kg
Step-by-step explanation:
Regular cakes:
1 dozen normal sponge cakes: 264 g plain flour
Vegetarian cakes:
1 dozen cakes: 264 g plain flour
4 eggs are replaced by 4 * 30 g of flour = 120 g flour
total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g
Proportion for regular cakes:
12 cakes to 264 g flour = 100 cakes to x grams flour
12/264 = 100/x
12x = 26400
x = 2200
2200 g flour for 100 regular cakes
Proportion for vegetarian cakes:
12 cakes to 384 g flour = 60 cakes to y grams flour
12/384 = 60/y
12y = 384 * 60
12y = 23040
y = 1920
1920 g flour for 60 vegetarian cakes
Total flour needed:
2200 g + 1920 g = 4120 g
4120 g * 1 kg/(1000 g) = 4.12 kg
Answer: 4.12 kg
Determine the critical value for a 98% confidence interval when the sample size is 12 for the t ‑distribution. Enter the positive critical value rounded to 3 decimal places.
Answer:
+2.718
Step-by-step explanation:
from the question,
the sample size is 12
therefore the degree of freedom,
df = 12 - 1
= 11
alpha = 1 - 0.98
= 0.02
this is because the confidence level is 98%
under the t distribution table, a degree of freedom of 11 and 0.02 alpha level = 2.718
the critical value t* = 2.718
I hope this helps!
16/4 + 56 – (3 + 4 - 1) =
Answer:
54Step-by-step explanation:
PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
We have to do operations by the Order of Operations(PEMDAS)
Parentheses:
Addition/Subtraction:
(7 - 1)
(6)
16/4 + 56 - 6
Multiplication/Division
4 + 56 - 6
Addition/Subtraction
60 - 6
54Which of the following is the solution to the equation 25^(z + 2) = 125? (6 points) Answer choices are 1) z = 5.5 2) z = 3.5 3) z = −2.5 4) z = −0.5
Step-by-step explanation:
a. z = 5.5
25 ^( 5.5 - 4 ) = 125
25 ^ (1.5) = 125
125 = 125
z = 5.5
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the average temperature for one week in Alaska are as follows: 10, 6, 9, 2, 0,3. what is the mean of these tempartures ? show all work.
Answer:
5
Step-by-step explanation:
We know that we have to add all numbers then divide it by how many numbers there are. So, 10 + 6 + 9 + 2 + 0 + 3 = 30. 30/6 = 5.
Tasha wants to measure the height of a tree that grows at an angle of 85° with respect to the ground.
When she is 80 feet away from the base of the tree she looks up. The angle from the ground to the top of
the tree is 25°. Approximately, how tall is the tree?
Answer: 35.9
Step-by-step explanation:
The tree is approximately 35.979 feet tall, computed using the sine rule.
What is the sine rule?The sine rule in a triangle can be shown as this.
A triangle ABC, with the values of the side BC = a, CA = b, and AB = b, follows the rule by:
(Sin A)/a = (sin B)/b = (sin C)/c.
How to solve the given question?In the question, we are informed about Tasha who is willing to measure the height of a tree, which grows at an angle of 85° with respect to the ground. Also, we are informed that when Tasha is 80 feet away from the base of the tree, then the angle from the ground to the top of the tree is 25°.
We are asked to find the height of the tree.
We first draw a triangle using the given details, AB being the tree, and C being the point where Tasha is.
We know ∠A = 180° - (∠B + ∠C) {By angle sum property of triangles)
or, ∠A = 180° - (85° + 25°) = 180° - 110° = 70°.
Now, by sine rule, we can say that:
(Sin A)/a = (sin B)/b = (sin C)/c.
or, (Sin 70°)/80 = (sin 85°)/b = (sin 25°)/c,
or, 0.93969262078/80 = 0.42261826174/c {We ignored the middle term as we only need the height of the tree, that is, c}
or, c = 0.42261826174*80/0.93969262078/80
or, c = 35.9792768309.
Therefore, the tree is approximately 35.979 feet tall, computed using the sine rule.
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Part F
I NEED HELP!
What is the geometric mean of the measures of the line segments A Dand DC? Show your work.
Answer:
AC2 = AB2 + BC2 ---> AC2 = 122 + 52 ---> AC = 13
AD / AB = AB / AC ---> AD / 12 = 12 / 13 ---> AD = 144/13
DC = AC - AD ---> DC = 13 - 144/13 ---> DC = 25/13
AD / DB = DB / DC ---> DB2 = AD · DC ---> DB2 = (144/13) · (25/13) ---> DB = 60/13
DB is the geometric mean of AD and DC.
Step-by-step explanation:
a rope is wound 50 times around a cylinder of radius 25cm. How long is the rope
Circumference of the cylinder :
C = 2 x pi x r
C = 2 x 3.14 x 25 = 157 cm
Multiply the circumference by number of wraps:
157 x 50 = 7,850 cm long ( 78.5 meters)
help with this will give bralienst pleaseeee
Answer:
D
Step-by-step explanation:
You can test this out with a number.
try dividing 23 by 8:
you will get 2 remainder 7 which works for the condition.
Note: Whenever you divide a number by x(other number) the remainder will always have to be to less than x:
The only one that applies to this aforementioned condition is 8.
Answer:
D
Step-by-step explanation:
The remainder can never be greater than the number by which it is divided
For example:
n = any number
n / 2 -> The remainder will never be greater than 2 (0 < remainder <2)
n / 3 -> The remainder will never be greater than 3 (0 < remainder <3)
n / 4 -> The remainder will never be greater than 4 (0 < remainder <4)
n / 5 -> The remainder will never be greater than 5 (0 < remainder <5)
n / 6 -> The remainder will never be greater than 6 (0 < remainder <6)
..... etc