Answer:
550
Step-by-step explanation:
165 x 100= 16500/30=550
What is the resulting polynomial when -7w² +13 is subtracted from -2w²+6w - 19?
Answer:
5w^2 + 6w - 32
Step-by-step explanation:
Subtract as needed and combine like terms
(-2w^2 + 6w - 19) - (-7w^2 +13) dont forget to distribute the negative
so you get this:
-2w^2 + 7w^2 = 5w^2
6w
-19 - 13 = - 32
your answer is 5w^2 + 6w - 32
hope this helps :)
Hi :)
Let's solve by combining like terms
——————————Combining like terms means you add or subtract
terms with the same variable (if any)terms with the same exponentSolve by combining like terms
[tex]\implies\darkblue\sf{-2w^2+6w-19-(-7w^2+13)}\\\implies\darkblue\sf{-2w^2+6w-19+7w^2-13}\\\implies\darkblue\sf{-2w^2+7w^2+6w-19-13}\\\implies\darkblue\sf{\underline{5w^2+6w-32}}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
An insurance company states that it settles 85% of all life insurance claims within 30 days. A consumer group asks the state insurance commission to investigate. In a sample of 250 life insurance claims, 203 were settled within 30 days.
a. Test whether the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%, at the 5% level of significance.
Using the z-distribution, it is found that since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the proportion is below 85%, that is:
[tex]H_0: p \geq 0.85[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the proportion is below 85%, that is:
[tex]H_0: p < 0.85[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.85, n = 250, \overline{p} = \frac{203}{250} = 0.812[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.812 - 0.85}{\sqrt{\frac{0.85(0.15)}{250}}}[/tex]
z = -1.68
What is the p-value and the conclusionUsing a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -1.68, the p-value is of 0.0465.
Since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.
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find the square roots by division method of 151,321
Answer: 389 is the square root.
Answer:
389 is the square root
Step-by-step explanation:
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what base could be written in the blank to make the exponential function model 15% decay ? y= (___) ^t\12
The base of the exponential function model in order to get 15% decay should be 0.85
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.
The first step would be figuring out the function's base.
The function's form should be, [tex]y=a*b^{t}[/tex]
Here,
'a' denotes the starting value.
'b' denotes the decrease rate.
't' denotes time.
According to the question, the exponential function model is,
[tex]y=b^{\frac{t}{12} }[/tex]
In order to get a 15% decay,
The base of the function should be (100-15)/100 = 0.85
Thus, Base of function(b) = 0.85
The exponential function model is written as:
[tex]y=0.85^{t/12}[/tex]
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The volume of a packing box is 5 - x cubic feet. The width of the box is x feet and the length is x - 2 feet
Answer:
Step-by-step explanation:
A hockey coach was taking her team out to a picnic lunch to celebrate their first win. She made 15 sandwiches, 6 of which were turkey.
If ants randomly chose to nibble on 6 of the sandwiches, what is the probability that exactly 3 of the chosen sandwiches are turkey?
The probability that exactly 3 of the chosen sandwiches are turkey is; 0.004
How to find the probability combination?We are given;
Total number of sandwiches = 15
Number of sandwiches that were turkey = 6
Now, she selects 6 of the sandwiches and we want to find the probability that exactly 3 are turkey.
Now, number of ways of selecting 6 sandwiches is; 15C6
Number of ways of selecting 3 turkey's out of the 6 chosen is; 6C3
Thus, the probability that exactly 3 of the chosen sandwiches are turkey is; 6C3/15C6 = 20/5005 = 0.004
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Graph the line passing through (−4,−1) whose slope is m=−4/5
the answer is (-4,-1) and (1,-5)
A map uses a scale of 1
cm = 5½ miles. In actual
distance, the entrances to
two parks are 24 miles
apart. How far apart are
they on the map?
Answer:
3.36 cm
Step-by-step explanation:
24 - 5 1/2 = 18.5
To find the distance on the map, we can set up a proportion:
1 cm / 5.5 miles = x cm / 18.5 miles
5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).
A "Shirley Temple" drink is made by a 5.
mixing 2 cups of 7-Up with 4 tablespoons
of grenadine syrup. Write a ratio of
grenadine syrup to 7-Up. (hint: 160 lstot of an
Tablespoons = 1 Cup)
The ratio of grenadine syrup to 7-Up will be 1:8.
How to find the ratio?From the information given, we are told that Shirley Temple" drink is made by a 5 mixing 2 cups of 7-Up with 4 tablespoons of grenadine syrup.
The ratio of grenadine syrup to 7-Up will be:
4 tablespoon : 2 cups
Note that 1 cup = 16 teaspoon
4 : (2 × 16)
= 4:32
= 1:8
Therefore, the ratio of grenadine syrup to 7-Up will be 1:8.
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if the diameter of a circular pond is x meter what is the measure of its circumference
πx
Step-by-step explanation:
well pi is defined as the ratio of a circle's circumference to its diameter so just πx
A lateral thoracic spine on a 33-cm patient is usually taken using 100 mA (large focal spot), 0.5 seconds, 86 kVp, 40-inch SID, 12:1 grid ratio. If the mA is increased to 400 to stop motion blur from tremors, which of the following technique changes will produce a radiographic density and contrast most similar to the original?
A 0.13 sec and a 86 kVp technical changes are the changes that would have to produce the radiographic density and the contrast that are more similar to the original.
What is the radiographic density?The radio graphic density can de defined to be the total amount or the overall darkening that can be found in a particular radiograph. This is usually known to have a certain type of density range that lies between 0.3 to 2.0 density.
When there is a density that is less than 0.3, the problem is basically because there is the issue of the density which would be found at the base and the fact that the film that is being used has fog in it.
It is known that based on the values that we have here the density and contrast would have to be of the given kvp of 86 and 0.13 seconds in order to be said to be similar to the original.
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What is the ordered pair of X' after point X (3, 4) is rotated 180°?
OX' (3,-4)
OX' (-3,-4)
OX' (-4, 3)
OX' (-4,-3)
35. Calculate the area of ARST if b = 29.
R
S
30°
1456.65 units²
841 units²
728.33 units²
364.16 units²
b
T
None of these answers are correct.
The area based on the information illustrated will be 825 unit².
How to illustrate the information?Your information is incomplete. Therefore, an overview will be given. It should be noted that area simply means the quantity which expresses the extent of the region on a plane as well as a curved surface. Based on this information, it should be noted that the area of a rectangle is given as:
Area = Length × Width
Let's assume that the width is 25 units and the length is given as 33 units.
Then, the area will be:
= Length × Width
= 33 × 25
= 825 units²
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T=235+980d
The torque, TTT, in newton-meters, on a diving board with a 100 kilogram weight placed "d" meters from the diving board's fulcrum is given by the equation above. How much torque in newton-meters is on the diving board when the weight is placed at the fulcrum?
Questions:
1. what does 980 in the equation represent?
2. Why is the answer 235?
The answer is 235 because the weight is placed at the fulcrum
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
1. What does 980 in the equation represent?The linear equation is given as:
T = 235 + 980d
A linear equation is represented as:
T = b + md
Where m represents the slope
So, we have
m = 980
This means that 980 represents the amount of Torque per meter
2. Why is the answer 235?When the weight is placed at the fulcrum, the value of d is 0
So, we have
T = 235 + 980d
Evaluate
T = 235 + 980 * 0
This gives
T = 235
Hence, the answer is 235 because the weight is placed at the fulcrum
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Using plane K, name a point that is not on the line.
Answer:
H
Step-by-step explanation:
Plane K is shown with two lines. Points on one of them are A, B, G. Points on the other one are G, M, N.
The point in plane K that is not shown on any line is point H.
Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
OA.
y=3x+4
OB. y=3x-14
OC. y=3x-4
OD. y=3x + 12
Answer: [tex]\Large\boxed{A.~y=3x+4}[/tex]
Step-by-step explanation:
Given information
Slope = 3
Point = (-3, -5)
Given the format of the equation
Slope-intercept form: y = mx + b
m = Slopeb = y-interceptSubstitute values into the equation
y = (3)x + b
y = 3x + b
Substitute the given point into the equation to get the value of [ b ]
(-5) = 3(-3) + b
-5 = -9 + b
b = -5 + 9
b = 4
Therefore, the equation of the line is [tex]\Large\boxed{y=3x+4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at rural hospitals have a lower waiting time? The 13 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.3 hours to be admitted into the hospital. The standard deviation for these 13 patients was 1.3 hours. What can be concluded at the the
α
= 0.01 level of significance level of significance?
For this study, we should use
Select an answer
The null and alternative hypotheses would be:
H
0
:
?
Select an answer
H
1
:
?
Select an answer
The test statistic
?
=
(please show your answer to 3 decimal places.)
The p-value =
(Please show your answer to 4 decimal places.)
The p-value is
?
α
Based on this, we should
Select an answer
the null hypothesis.
Thus, the final conclusion is that ...
The data suggest the population mean is not significantly lower than 7 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.
The data suggest the populaton mean is significantly lower than 7 at
α
= 0.01, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 7 hours.
The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly lower than 7 hours at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 7 hours.
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the test statistic?The test statistics can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the number of hours.For this study, we should use t-test and the null and alternative hypotheses would be given by:
H₀: μ = 7
H₁: μ < 7
[tex]t=\frac{6.3\;-\;7}{\frac{1.3}{\sqrt{13} } }\\\\t=\frac{-0.7}{\frac{1.3}{3.6056 } }[/tex]
t = -0.7/0.3606
t = -1.941.
For the p-value, we have:
P-value = P(t < -1.9412)
P-value = 0.0381.
Therefore, the p-value (0.0381) is greater than α = 0.01. Based on this, we should fail to reject the null hypothesis.
Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.
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Simplify the following expression:
( 4 + 5i ) / 4i
Select one:
a.
( 5 + 4i ) / 4
b.
( 5 - 4i ) / 4
c.
( 5i + 4i ) / 4
d.
( 5i - 4 ) / 4
Answer: B
Step-by-step explanation:
[tex]\frac{4+5i}{4i}\\ \\ =\frac{1}{4} \left(\frac{4+5i}{i} \right)\\\\=\frac{1}{4}((-i)(4+5i))\\\\=\frac{1}{4}(-4i-5i^2)\\\\=\frac{5-4i}{4}[/tex]
what is the area of a polygon with verticies of (-2,2), (3,2), (7,-5) and (-2,-5)
Check the picture below.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=9\\ h=7 \end{cases}\implies \begin{array}{llll} A=\cfrac{7(5+9)}{2}\implies A=\cfrac{7(14)}{2} \\\\\\ A=49 \end{array}[/tex]
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 20 trials and got the following results.
Using the probability concept, we have that:
a) The experimental probability is of 0.75 = 75%.
b) The theoretical probability is of 0.5 = 50%.
c) As the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials. A theoretical probability is calculated before any trial, and as the number of trials increase, the experimental and theoretical probabilities get closer.
From the table, there were 20 trials, and 2 + 3 + 4 + 4 + 2 = 15 resulted in even numbers, hence the experimental probability is:
p = 15/20 = 0.75 = 75%.
For a fair machine, even and odd numbers should be equally as likely, hence the theoretical probability is of 0.5 = 50%.
For item c, we have that as the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
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For which interval does this quadratic inequality hold true?
x²-4x-12 ≤0
A. (2,-6)
B. (0,4)
C. (-2, 2)
D. (-2, 6)
Answer:
D
Step-by-step explanation:
x²-4x-12≤0
x²-6x+2x-12≤0
x(x-6)+2(x-6)≤0
(x-6)(x+2)≤0
x=6,-2
∴ value of x lies between -2 & 6
3 1/3(2 1/5x-4 2/3) - 5 5/6=0, solve please
Based on the task content given; the solution to the equation for x 3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0 is 2 203/231
Simplification3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0
open parenthesis(3 1/2 × 2 1/5x) - (3 1/2 × 4 2/3) - 5 5/6 = 0
(7/2 × 11/5x) - (7/2 × 14/3) - 35/6 = 0
77/10x - 98/6 - 35/6 = 0
77/10x = 98/6 + 35/6
77/10x = 98+35 / 6
77/10x = 133/6
x = 133/6 ÷ 77/10
= 133/6 × 10/77
= 1330/462
x = 2 406/462
= 2 203/231
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Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
(–∞, –3)
(–∞, 3)
(–3, ∞)
(3, ∞)
The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)
on what interval is the function positive?The function is positive when g(x) > 0.
Then we need to solve:
∛(x - 3) > 0
We can directly remove the cubic root, because it does not affect the sign of the argument, then:
x - 3 > 0
x > 3
The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)
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The interval which the function is positive is (3, ∝)
How to determine the positive interval?
The equation of the function is given as:
g(x) =∛x - 3
Set the radical greater than 0
x - 3 > 0
Add 3 to both sides of the inequality
x > 3
Express as an interval notation
(3, ∝)
Hence, the interval which the function is positive is (3, ∝)
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The graph of a function g is shown below.
Use the graph of the function to find its average rate of change from x=-2 to x=4.
Simplify your answer as much as possible.
1-10
Answer: -2
Step-by-step explanation:
The graph passes through (-2, 3) and (4, -9).
So, the average rate of change is [tex]\frac{-9-3}{4-(-2)}=\boxed{-2}[/tex]
classify the numbers in the image to be either a whole number integer rational number irrational number real number
A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days.
With the use of formula, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams
Word Problem Leading to Exponential FunctionFirst analyze the problem and represent them in exponential function. The decay rate is different from increase rate with minus and plus sign.
Given that a tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Let
I = initial amount injected = 0.9 gramsR = decay rate = 1.15%t = number of days = 60 daysA = the remaining amount of Iodine - 125An exponential model representing the amount of Iodine-125 remaining in the tumor after t days will be
A = I( 1 - R%)^t
Let us use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days by substituting all the given parameters into the formula
A = 0.9 ( 1 - 1.15/100)^60
A = 0.9 ( 1 - 0.0115)^60
A = 0.9 ( 0.9885)^60
A = 0.9 x 0.4995
A = 0.45 grams
Therefore, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams
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Instructions: Match the following data with the correct stem and leaf.
Helped need please
Based on the stem and leaf plots given, the correct stem and leaf plot for the first table on per capita income is the third stem and leaf diagram.
For the table on the basketball tornament, the correct stem and leaf plot would be the last one.
How are stem and leaf plots used?First look at the key to the bottom right of the plot to see how to interpret the data.
The key on the third stem and lead plot says 1 I 2 = 12,000. This means that every steam and lead pairing is in thousands.
Based on the income per capita being in thousands, this is the most likely stem and lead plot for the first table on income per capita.
The second table about basketball tornament appearances is on single and double digits. Only a small stem and leaf key will do.
Look at the number of appearances. The minimum is 1. On a stem and leaf, this is shown as 0 I 1. Options A and B don't have this so we go to Options C and D.
As established, Option C is for data in their thousands so it is out. The correct stem and leaf plot is therefore Option D.
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What is the converse of the conditional statement?
If x is even, then x + 1 is odd.
O If x is not even, then x + 1 is not odd.
O If x + 1 is odd, then x is even.
If x + 1 is not odd, then x is not even.
OIf x is even, then x + 1 is not odd.
Mark this and return
Save and Exit
Next
Submit
The correct answer is If x + 1 is odd, then x is even.
What is the converse of the conditional?A conditional statement's opposite is produced when the hypothesis and conclusion are switched around. The conditional statement is known as p q in geometry. q p is how people refer to the Converse.One can obtain the contrary assertion by switching "p" and "q locations "in the condition. An example of a condition is "If Cliff is thirsty, then she drinks water." If Cliff drinks water, then she is thirsty, is the converse of the first sentence.The four primary varieties of conditional phrases are Zero Conditional, First Conditional, Second Conditional, and Third Conditional.The converses of the conditional statement:
"If q then p" provides the converse statement to the conditional expression "If p then q."
The converse of the conditional statement is If x + 1 is odd, then x is even.
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On a map, 3 inches represents 50 miles. Which proportion can be used to find the actual distance represented by 5 inches on the map?
StartFraction 3 over 50 EndFraction = StartFraction x over 5 EndFraction
StartFraction 3 over 50 EndFraction = StartFraction 5 over x EndFraction
StartFraction 3 over x EndFraction = StartFraction 50 over 5 EndFraction
StartFraction x over 3 EndFraction = StartFraction 50 over 5 EndFraction
The correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Given that 3 inches on a map represents 50 miles.
We are told to find the proportion which can be used to represent 5 inches.
Multiplication is basically finding the product of two numbers but it can be used to convert the units also.
If 3 inches represents 50 miles then,
1 mile=50/3
Multiply both sides by 5.
5 miles=5*50/3
If we see the options then we will get that the most appropriate and correct option which represents 5 inches is that start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Hence the correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
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Answer:
B
Step-by-step explanation:
3/50 = 5/x
What is the next number in the following sequence 0 0 1 2 2 4 3 6 4 8 5
Answer:
10
Step-by-step explanation:
the sequence follows the rule of adding the number and then the number -1 depending on the number before it. for example, you can see in order to get from 2 to 2, it adds 0 or subtracts by 0. After that to get from 2 to 4, you add 2. After that, you subtract 1 from 2 and you subtract that number which is 1 from 4 to get 3 and so on. Following that rule, you get 10 as the next number in the sequence