Answer:
1.24
Step-by-step explanation:
because 1.24>1.215>0.365>0.095
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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What is the quotient of 7.536\times 10^77.536×10
7
and 7.85 \times 10^27.85×10
2
expressed in scientific notation?
The value of Quotient from the given terms is 9.6* 10^8
According to the statement
we have given that the two terms and we have to find the quotient of the these terms.
So, we know that the
Quotient is a the number resulting from the division of one number by another.
And for find the quotient we have to divide the terms with each other.
So, The given terms are [tex]7.536*10^7[/tex]and [tex]7.85*10^2[/tex]
divide both terms with each other.
Quotient = [tex]\frac{7.536*10^7}{7.85*10^2}[/tex]
Then
The value of quotient becomes
Quotient = [tex]0.96 * 10^9[/tex]
After removing the decimal from the answer it will become
Quotient = [tex]9.6* 10^8[/tex].
So, The value of Quotient from the given terms is 9.6* 10^8
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Answer: its 7.85x10^-9
Step-by-step explanation:
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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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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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 "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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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]
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]
simplify
a(cube)-1000b(cube)
64a(cube)-125b(cube)
The simplification of a³ - 1000b³ and 64a³ - 125b³ is (a - 10b) × (a² + 10ab + 100b²) and 4a - 5b) • (16a² + 20ab + 25b²) respectively.
SimplificationQuestion 1: a³ - 1000b³
a³ - b³
= (a-b) × (a² +ab +b²)
1000 is the cube of 10 a³ is the cube of a¹b³ is the cube of b¹So,
(a - 10b) × (a² + 10ab + 100b²)
Question 2: 64a³ - 125b³
a³ - b³
= (a-b) × (a² +ab +b²)
64 is the cube of 4 125 is the cube of 5 a³ is the cube of a¹b³ is the cube of b¹So,
(4a - 5b) • (16a² + 20ab + 25b²)
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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.
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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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
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]
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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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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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
The standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
How to illustrate the information?From the information given, it was stated that the students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury.
Based on the information given, it should be noted that the appropriate thing to do is to find the z score for the 75th percentile.
This will be looked up in the distribution table. In this case, the value is 0.674. Therefore, standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
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A shipping company charged $15 to ship a package and 5% to insure the package.What was the total cost to ship this particular item?
Answer:
5% of 15 is 0.75 i think
Step-by-step explanation:
15/5% is 0.75
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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4899 x 67 show your work
Answer:
328,233
Step-by-step explanation:
Use the algorithm method.
4 8 9 9
× 6 7
3 6 6 6
3 4 2 9 3
2 5 5 5
2 9 3 9 4 0
1 1 1
3 2 8 2 3 3
⇒ 328,233
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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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
Graph the line passing through (−4,−1) whose slope is m=−4/5
the answer is (-4,-1) and (1,-5)
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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classify the numbers in the image to be either a whole number integer rational number irrational number real number
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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follow the steps to find the area of the shaded region. 14 46 14
The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.
How to calculate the area of the sector?The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is
A = (θ/360) πr² sq. units
How to calculate the area of a triangle with an angle?The area of the triangle with measures of two sides and an angle between them is
A = 1/2 × a × b × sinC sq. units
Where a and b are the lengths of sides and ∠C is the angle between those sides.
Calculation:It is given that,
The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².
Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,
Area of the shaded region = Area of the sector - Area of the triangle
⇒ 78.6794 - 70.4956
⇒ 8.1838 cm²
Therefore, the required area of the shaded region is 8.1838 sq. cm.
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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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Somebody help me with this please
Answer: 9 units
Step-by-step explanation: R is at -7 and is at 2. Think of how far away -7 is from 2. -7+9=2.
Answer:
9 units
Step-by-step explanation:
Length of a segment RV is a difference of values of V and R. According to the number line, R is -7 and V is 2.
The difference or change in two values is 2 - (-7) = 2 + 7 = 9 units.
Henceforth, the segment RV is 9 units.
A spinner is divided into five sections numbered 1 through 5. Juana records the number the spinner lands on for each of 50 spins. She computes and graphs the relative frequencies for each number. Which of the following describes the probability distribution?
A bar graph entitled Relative Frequency of Numbers Spun has x on the x-axis and Probability on the y-axis. The probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12.
constant
symmetric
negatively skewed
positively skewed
If the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12 then the graph is somewhat positively skewed and then becomes constant.
Given the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12.
We are required to find whether the graph is constant,symmetric ,negatively skewed or positively skewed.
We can say that the graph is somewhat positively skewed and then it becomes constant.
Positively skewed graph is a graph in which more values exist at the left side of the graph means the tail is started in end.
Constant graph is a graph in which all the values are equal to each other.
In our case except the probability of 1 all the values are 0.12 and the probability of 1 is 0.5.
Hence if the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12 then the graph is somewhat positively skewed and then constant.
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Answer:
constant
Step-by-step explanation:
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).