Answer:
k = 13The smallest zero or root is x = -10
Step-by-step explanation:
you can write "x^2" to mean "x squared"
f(x) = x^2+3x-10
f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5
f(x+5) = (x^2+10x+25)+3(x+5)-10
f(x+5) = x^2+10x+25+3x+15-10
f(x+5) = x^2+13x+30
Compare this with x^2+kx+30 and we see that k = 13
Factor and solve the equation below
x^2+13x+30 = 0
(x+10)(x+3) = 0
x+10 = 0 or x+3 = 0
x = -10 or x = -3
The smallest zero is x = -10 as its the left-most value on a number line.
Use the quotient property to rewrite log_(10)(x/(100,000))
Answer:
log_10(x) - log_10(100000)
Step-by-step explanation:
[tex]log_{10}(\frac{x}{100000} )\\log_{10}(x) -log_{10}(100000)\\[/tex]
Using the quotient property, log_{10} \dfrac{x}{(100,000)} = log_{10}(x) - log_{10}(100000).
How to find quotient of a over b/c?WE can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
Thus,
[tex]\dfrac{a}{\frac{b}{c}} = a \times \dfrac{1}{\frac{b}{c} } = a \times \dfrac{c}{b} = \dfrac{a \times c}{b}[/tex]
We have to Use the quotient property to rewrite;
[tex]log_{10} \dfrac{x}{(100,000)}[/tex]
SO, [tex]log_{10} \dfrac{x}{(100,000)} = log_{10}(x) - log_{10}(100000)[/tex]
Therefore, Using the quotient property, log_{10} \dfrac{x}{(100,000)} = log_{10}(x) - log_{10}(100000).
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Write a rule for the geometric sequence with the given description
Answer:
a. [tex] a_n = -3(5^{n - 1}) [/tex]
b. [tex]a_n = 72(3^{1 - n})[/tex]
Step-by-step explanation:
a.
[tex] a_1 = -3 [/tex]
[tex] a_2 = -3(5^1) [/tex]
[tex] a_3 = -3(5^2) [/tex]
Notice that in each term, the exponent of the 5 is 1 less than the term number.
The general term is
[tex] a_n = -3(5^{n - 1}) [/tex]
b.
[tex] a_1 = 72 [/tex]
[tex] a_2 = 72(\dfrac{1}{3})^1 [/tex]
[tex] a_3 = 72(\dfrac{1}{3})^2 [/tex]
Notice that in each term, the exponent of the 1/3 is 1 less than the term number.
The general term is
[tex] a_n = 72(\dfrac{1}{3})^{n - 1} [/tex]
[tex] a_n = 72(\dfrac{1}{3^{n - 1}}) [/tex]
[tex] a_n = 72(3^{1 - n}) [/tex]
9x-3=87 what is the anwser
Answer:
x=10
Step-by-step explanation:
9x-3=87
add 3 to both sides
9x=90
divide by 9 on both sides
x=10
Answer:
x=10
Step-by-step explanation:
9x-3=87
you add 3 to both sides
9x-3(+3)=87(+3)
which equals
9x=90
90/9= 10
answer:
x =10
I hope this helped!
A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks
Answer:
The number of mice that will be infected next week are 130 while
The number of mice that will be infected in 3 weeks are 111
Step-by-step explanation:
From the information given , the researcher is studying the spread of a virus in a population of 1000 laboratory mice. i.e, n = 1000
Number of infected = 300
Non infected = 1000 - 300 = 700
Probability an infected mouse will overcome = 80% = 0.8
Probability a noninfected mouse becomes infected = 10% = 0.10
The number of infected that will overcome = 0.8 * 300 = 240
The number of non infected that will become infected = 0.1 * 700 = 70
The number that will be infected on the first week =
300 - 240 + 70
= 130
Number that will be healthy on the first week =
700 + 240 - 70
= 870
Calculating for week 2:
The number of infected that will overcome = 0.8 * 130 = 104
The number of non infected that will become infected = 0.10 * 870 = 87
The number that will be infected on the second week =
130 - 104 + 87
= 113
Number that will be healthy on the second week =
870 + 107 - 87
= 887
Calculating for week 3:
The number of infected that will overcome = 0.8 * 113 = 90.4
The number of non infected that will become infected = 0.10 * 887 = 88.7
The number that will be infected on the third week =
113 - 90.4 + 88.7
= 111.3 ≈ 111
Number that will be healthy on the third week =
887 + 90.4 - 88.7
= 888.7 ≈ 889
From our calculations, the number of mice that will be infected next week are 130
The number of mice that will be infected in 3 weeks are 111
Determine if the point (2, 6) is on the graph of
Answer:
it is not on the graph
Step-by-step explanation:
Put the given values into the equation and see if it is true:
-2(2) +1/3(6) = -1
-4 +2 = -1 . . . . . . . .FALSE
The point is not on the graph of the equation.
A random sample of 95 vehicles is taken from a large parking lot at an office park. Below is the type of each vehicle, and whether it is owned or leased by the driver. A chi-square test will be conducted to determine if there is an association between type of vehicle and method of obtaining the vehicle. Which of the following expressions represents the expected count of leased SUVs? Car 29 21 Owned Leased SUV 20 10 1 Truck 1 4 O (A) 10 (B) (C) (35)(30) (D) (10-1.1.1) 111 (E) (11.1-10)
Answer:
C
Step-by-step explanation:
The expression that represents the expected count of leased SUVs from the given data is; C: (35)(30)/95
How to utilize chi square test?We are given;
sample size; n = 95 vehicles
From the table gotten online, we see that;
There are 20 owned SUV's and 10 leased SUV's
From the chi square results gotten from online calculator, we can say that; the expected count of leased SUVs is gotten as;
(35)(30)/95
Therefore we can conclude that the expression that represents the expected count of leased SUVs is option C.
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Ollivanders stuffed bear shop has 456 bears in stock exactly half of them Are made from wool how many wool does Mr.oillvander have in stock
Answer:
228 of them are made from wool, but there is no enough information to determine how many would he has in stock.
Step-by-step explanation:
Mr Ollivander's stuffed bear shop has 456 bears in stock, and exactly half of them are made from wool, this means that 1/2 of 456 are made from wool
1/2 of 456 = 1/2 × 456 = 456/2 = 228.
That is 228 of them are made from wool.
However, nothing tells us that this is all he has in his stock. There is no information available to determine how many would he has in stock.
The average hourly wage for a high school student in Illinois is $8.25 per hour with a standard deviation of $.25. Assume hourly wages vary normally.
A) Determine the margin of error for this scenario.
B) For the previous question you just answered, construct a 95% confidence interval for the hourly wage for a high school student.
C) For the 95% confidence interval you just constructed, does an hourly wage of $9.15 fall within that acceptable range?
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: hourly wage of a high school student
X~N(μ;σ²)
X[bar]= $8.25
σ= $0.25
For a 95% CI for the average hourly wage for 1 high school student:
For this exercise you have to consider the sample size n=1
a) The margin of error of the CI is calculated as:
d= [tex]Z_{1-\alpha /2}[/tex] * σ
1-α: 0.95 ⇒ α:0.05
1-α/2:0.975
[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
d= 1.96 * 0.25= 0.49
b)
The formula for the interval is
X[bar] ± [tex]Z_{1-\alpha /2}[/tex] * σ
[8.25 ± 0.49]
[7.76; 8.74]
With a 95% you'd expect the interval $[7.76; 8.74] to include the average hourly wage of one high school student in Illinois.
c)
Te calculated interval is $ [7.76; 8.74] the value $9.15 does nor fall within that acceptable range.
I hope this helps!
Gloria earned a total of $810 over the summer. She earned $162 babysitting and the rest
from mowing lawns. Which bar model and solution represent x, the amount of money Gloria
earned mowing lawns?
Let x represent the amount of money Gloria earned mowing lawns.
We have been given that Gloria earned a total of $810 over the summer. She earned $162 babysitting and the rest from mowing lawns.
The total amount earned by Gloria would be amount earned from baby sitting and lawn mowing that is [tex]x+162[/tex].
Now we will equate total earnings of Gloria by 810 as:
[tex]x+162=810[/tex]
[tex]x+162-162=810-162[/tex]
[tex]x=648[/tex]
Therefore, Gloria earned $648 from mowing lawns.
Answer:
Gloria earned $648 from mowing lawns
Step-by-step explanation:
a connection between two sets of
numbers in which the first set of
numbers (the x values) is linked to
the second set of numbers (they
values)
Jk
Answer:
I dont know sorry
Step-by-step explanation:
Answer:
its a relation
Step-by-step explanation:
What do scientist mean by flattening the curve and why is it important?
Answer:
MRCORRECT has answered the question
Step-by-step explanation:
Inhibiting new infections to reduce the number of cases at any given time—known as "flattening the curve"—allows healthcare services to better manage the same volume of patients.
Answer:
I believe it means to slow down the virus spreading to other people and to stay safe, avoid contact, and wash your hands to stop too many people from going into the hospital.
Step-by-step explanation:
Side XY of triangle XYZ is extended to point W, creating a linear pair with <WYZ and <XYZ. What is the value of x?
Answer:
80
Step-by-step explanation:
I just did this and its right!
Answer:
80
Step-by-step explanation:
step-by-step explanation is xy xyz wyz xyz 80
What’s the correct answer for this?
Can anyone help me with this?
Answer:
35 yards
Step-by-step explanation:
20yd+15yd
you add 20yd and the 15yd and that is your area.
Tyrianne next solved a quadratic equation her work shown below in which step did Tyrianne make an error 1/2(x+4)^2-3=29
Step 1
Answer:
step 2
Step-by-step explanation:
khan academy
Mercury is a heavy metal that can cause severe health problems in even small concentrations. Fish and shellfish efficiently concentrate mercury into their flesh, so it is important to monitor seafood for its mercury content. An extensive study conducted in 1980 concluded that the mean mercury level in oysters from the White Bear estuary was 0.020 parts per million (ppm) with a standard deviation ppm. In 2012, a sample of 40 oysters from the same estuary exhibited a mean mercury concentration of . Can you conclude that the 2012 mercury concentration is lower than in 1980? Use the level of significance.
Answer:
The overview of the problem is listed in the segment below on the explanation.
Step-by-step explanation:
The given values are:
Sample mean, [tex]\bar{Z}=0.017[/tex]
The hypothesized mean value, [tex]\mu_{0}=0.02[/tex]
Population standard deviation, [tex]\sigma=0.036[/tex]
As we know, the status of the test is as follows:
⇒ [tex]z^* = \frac{\bar X - \mu_0}{\frac{\sigma}{\sqrt{n}}}[/tex]
On putting the values, we get
⇒ [tex]= \frac{0.017 - 0.02}{\frac{0.036}{\sqrt{40}}}[/tex]
⇒ [tex]=-0.5357[/tex]
Now, even though this is a one-sided check, here so the p-value is measured as:
[tex]p=P(Z<-0.5357)[/tex]
[tex]=0.2[/tex]
Consequently p-value > 0.05 the check isn't relevant so there is no data to suggest that perhaps the concentration of mercury fallen from 1980 until 2012.
George calculated the distance between (2, 4) and (6, 3) using the distance formula. His work is shown below. 1. d = StartRoot (6 minus 2) squared + (3 minus 4) squared EndRoot. 2. d = StartRoot (4) squared + (negative 1) squared EndRoot. 3. d = StartRoot 16 + 1 EndRoot. 4. d = StartRoot 17 EndRoot Analyze George’s work. Is he correct? If not, what was his mistake? Yes, he is correct. No, he substituted values in the wrong places. No, he didn’t use the proper order of operations. No, he evaluated the powers incorrectly. will mark brainliest
Answer:
Yes, he is correct
Step-by-step explanation:
d = sqrt[(6-2)² + (3-4)²]
d = sqrt[4² + (-1)²]
d = sqrt(16 + 1)
d = sqrt(17)
Answer:
A
Step-by-step explanation:
Yes he is correct.
he didn't substitute the values in the wrong places.
he did use the proper order of operations.
he didn't evaluate the powers incorrectly.
Therefore, A is correct.
At the local bookstore, 4 paperback books cost $20. The table below represents the amount of books compared to the cost. Which ordered pairs could also be included in the table based on the information given?
Answer:
80 books = $400
Step-by-step explanation:
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. (a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03? Use a 95% confidence level. (Round your answer up to the nearest whole number.)
Answer:
A sample size of 657 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
In the past, 19% of all homes with a stay-at-home parent had the father as the stay-at-home parent.
This means that [tex]\pi = 0.19[/tex]
(a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03?
A sample size of n is needed.
n is found when [tex]M = 0.03[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.19*0.81}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.19*0.81}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.19*0.81}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.19*0.81}}{0.03})^{2}[/tex]
[tex]n = 656.91[/tex]
Rounding up to the nearest whole number.
A sample size of 657 is needed.
Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor’s. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. For the Gibbs brand, the population standard deviation of the sample is 2.3 pounds. A sample of 55 babies using the competitor’s brand revealed a mean increase in weight of 8.1 pounds. The population standard deviation is 2.9 pounds. At the .05 significance level, can we con- clude that babies using the Gibbs brand gained less weight? Compute the p-value and interpret it.
Answer:
[tex]z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936[/tex]
The p value can be founded with this formula:
[tex]p_v =P(z<-0.936)=0.175[/tex]
Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor
Step-by-step explanation:
Information given
[tex]\bar X_{1}=7.6[/tex] represent the mean for Gibbs products
[tex]\bar X_{2}=8.1[/tex] represent the mean for the competitor
[tex]\sigma_{1}=2.3[/tex] represent the population standard deviation for Gibbs
[tex]\sigma_{2}=2.9[/tex] represent the sample standard deviation for the competitor
[tex]n_{1}=40[/tex] sample size for the group Gibbs
[tex]n_{2}=55[/tex] sample size for the group competitor
[tex]\alpha=0.05[/tex] Significance level provided
z would represent the statistic
Hypothesis to verify
We want to check if babies using the Gibbs brand gained less weight, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}< 0[/tex]
The statistic would be given by:
[tex]z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936[/tex]
The p value can be founded with this formula:
[tex]p_v =P(z<-0.936)=0.175[/tex]
Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor
Aiden wanted to model -15 + 15 = 0 on the number line. He first drew an arrow 15 units long starting from zero that pointed to the left. He then draws another arrow 15 units long starting from zero that points to the right. What error did Aiden make?
A. The first arrow he drew should have pointed to the right to represent -15.
B. The second arrow he drew should have pointed to the left to represent 15.
C. The first arrow he drew should have started at -15 instead of 0.
D. The second arrow he drew should have started at -15 instead of 0.
Answer:
I think it's D
Step-by-step explanation:
The number never goes over 0 so there is no need to put anything above 0
Answer:
the answer is D. The second arrow he drew should have started at -15 instead of 0.
Step-by-step explanation:
was on a test I took and got 100
Which description matches finding the volume of the solid ?
Square prism + Triangular prism. Hope it helps.
a rectangular rug measures 8 feet long and 12 feet wide . what is the area of the rug
Answer:
96 square feet
Step-by-step explanation:
Area= length x width
So for the rug it would be 12x8
12x8=96
Convert the angle \theta=260^\circθ=260
∘
theta, equals, 260, degrees to radians.
Express your answer exactly.
\theta=θ=theta, equals
radians
Question:
Convert the angle θ=260° to radians.
Express your answer exactly.
θ = ___ radians
Answer:
260° = 13π/9 or 4.54 rad
Step-by-step explanation:
Given
θ=260°
Required
Convert from degree to radians
To convert an angle in degrees to radians, we simply follow the steps below.
1° = 1 * π/180 rad
Replace the 1° with x
So,
x° = x * π/180 rad.
Now, we assume that x = 260
This means that we substitute 260 for x. This gives
260° = 260 * π/180
260° = 260π/180
Divide numerator and denominator by 20
260° = 13π/9
We can leave the answer in this form or solve further.
Take π as 22/7. This gives
260° = 13/9 * 22/7
260° = 286/63
260° = 4.5396825397
260° = 4.54 rad (Approximated)
The value of an angle 260 degree into radians is,
⇒ 260 degree = 13π/9 radians
WE have to given that,
To convert an angle 260 degree into radians.
Now, WE know that;
1 degree = π/180 radians
Hence, We can convert an angle 260 degree into radians as,
1 degree = π/180 radians
260 degree = 260 x π/180 radians
260 degree = 13π/9 radians
Thus, WE get;
260 degree = 13π/9 radians
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Let a = 60. What is the value of a ÷ 5? equation
Answer:
12
Step-by-step explanation:
Just substitute 60 for a and divide it by 5
Ta Da!!
PLEASE HELP SOLVE FOR ‘X’!!!
Answer:
x= 10
Step-by-step explanation:
1/5 x -2/3 = 4/3
Add 2/3 to each side
1/5x -2/3 +2/3 = 4/3 +2/3
1/5x = 6/3
1/5x = 2
Multiply each side by 5
1/5x * 5 = 2*5
x = 10
solve the system of equations
Answer:
r=idk
y=idk
Step-by-step explanation:
which expresion has a valume of 7/12
Answer:
1/1 x 7/1 x 1/12
Is there any options?
Step-by-step explanation:
Answer:6/8 adding 1/4
Step-by-step explanation: Because im right probably
We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is 0.02. H0: 50% of community college students plan to vote in the next presidential election. Ha: More than 50% of community college students plan to vote in the next presidential election. What can we conclude
Answer:
we can conclude that more than 50% of community college students plan to vote in the next presidential election
Step-by-step explanation:
Decision Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Null hypothesis H0: 50% of community college students plan to vote in the next presidential election
H0: p = 0.50
Ha: More than 50% of community college students plan to vote in the next presidential election
Ha: p > 0.50
P-value = 0.02
From the decision rule;
Since the p-value for this study is less than the significance level.
0.02 < 0.05
So, we reject the null hypothesis, there is enough evidence to reject the null hypothesis. We thereby accept the alternative hypothesis.
Therefore, we can conclude that more than 50% of community college students plan to vote in the next presidential election
A sculpture sits on a pedestal in the shape of a square prism. The side lengths of a base of the prism are 3 feet. The height of the prism is 4 feet. The museum director wants to cover all but the underside of the pedestal with foil that costs $0.22 per square foot. How much will the foil cost?
Answer:
Total cost of covering the pedestal is $12.54.
Step-by-step explanation:
The pedestal is a square prism so top and bottom are of square shape.
Hence, we have here length = width
We know that the Total Surface Area of a Prism is:
[tex]\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)[/tex]
Where l is length,
w is width and
h is height of prism
We know that here w = l = 3 feet
and h = 4 feet
Also, underside of pedestal is not to be covered.
The underside of pedestal is square type.
So,
[tex]\text{Required Total Surface Area = } l\times w+ 2\times w \times h+2\times h \times l[/tex]
[tex]\Rightarrow 3 \times 3 + 2 \times 3 \times 4 + 2 \times 3 \times 4\\\Rightarrow 9 + 24 + 24\\\Rightarrow 57\ ft^{2}[/tex]
Cost of cover per square foot = $ 0.22
Total cost of [tex]57\ ft^{2}[/tex] [tex]\Rightarrow 0.22 \times 0.57 = \$12.54[/tex]
