(a)whats is the value of x
(b) what is the measure of angle B
[tex]cdb = 8 \\ x = 4 \\ by \: pythagoras \: theorem \\ 8 {}^{2} = 4 {}^{2} + x{}^{2} \\ 64 = 16 + x {}^{2} \\ 64 - 16 = x {}^{2} \\ 48 = x{}^{2} \\ \sqrt{48 } = x\\ angle \: b = 60 \\ angle \: of \: equilateral \: triangle \: equal \: 60[/tex]
Two people start biking from the same point. One heads east at 13 mph, the other south at 18 mph. What is the rate at which the distance between the two people is changing after 25 minutes and after 35 minutes? What is the rate at which the distance between the two people is changing after 25 minutes?
Answer:
[tex]22.21\ \text{mph}[/tex]
[tex]22.2\ \text{mph}[/tex]
Step-by-step explanation:
[tex]\dfrac{da}{dt}=13\ \text{mph}[/tex]
[tex]\dfrac{db}{dt}=18\ \text{mph}[/tex]
[tex]\dfrac{dc}{dt}[/tex] = Rate at which the distance between the two people is changing
At 25 minutes
[tex]a=13\times \dfrac{25}{60}=5.417\ \text{miles}[/tex]
[tex]b=18\times \dfrac{25}{60}=7.5\ \text{miles}[/tex]
[tex]c=\sqrt{5.417^2+7.5^2}\\\Rightarrow c=9.25\ \text{miles}[/tex]
Distance between the two people is
[tex]c^2=a^2+b^2[/tex]
Differentiating with respect to time we get
[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{5.417\times 13+7.5\times 18}{9.25}\\\Rightarrow \dfrac{dc}{dt}=22.21\ \text{mph}[/tex]
Distance between the two people is changing at a rate of [tex]22.21\ \text{mph}[/tex].
At 35 minutes
[tex]a=13\times \dfrac{35}{60}=7.583\ \text{miles}[/tex]
[tex]b=18\times \dfrac{35}{60}=10.5\ \text{miles}[/tex]
[tex]c=\sqrt{7.583^2+10.5^2}\\\Rightarrow c=12.95\ \text{miles}[/tex]
Distance between the two people is
[tex]c^2=a^2+b^2[/tex]
Differentiating with respect to time we get
[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{7.583\times 13+10.5\times 18}{12.95}\\\Rightarrow \dfrac{dc}{dt}=22.2\ \text{mph}[/tex]
Distance between the two people is changing at a rate of [tex]22.2\ \text{mph}[/tex].
A graph of is shown on the grid.
What are the zeros of f?
Answer:
no graph is provided, the zeros of f cannot be found without a graph
Step-by-step explanation:
Find the lateral surface 14ft area of the 2ft cylinder. Round your answer to the nearest tenth if necessary.
Answer:
616 square feet
Step-by-step explanation:
Lateral surface area of a cylinder can be determined by;
Lateral surface area = 2[tex]\pi[/tex]rh
where: r is its radius, and h is its height.
Given in the question that the height of the cylinder is 14 feet and of radius 2 feet, then;
Lateral surface area = 2[tex]\pi[/tex]rh
= 2 x [tex]\frac{22}{7}[/tex] x 2 x 14
= 2 x 22 x 2 x 7
= 616
Lateral surface area = 616 square feet
Thus, the lateral surface area of the cylinder is 616 square feet.
Cody bought two burgers and two small fries for $14. Mary bought three burgers and four small fries for $23. How much does one burger cost?
Answer:
the same as these 5 points, $5 for a burger
Step-by-step explanation:
Question
What is the value of x in the diagram?
A. x=2
B. x=3
C. x=5
D. X=8
Answer:
B
Step-by-step explanation:
The radius of a circle is 6 m. Find its area in terms of π.
Answer:
A=πr^2
22/7×6×6
=113 1/7
Suppose Salma borrows $3500 at an interest rate of 9% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
si
(b) Find the amount owed at the end of 2 years.
$
?
Answer:
(a) The amount owed At the end of 1 year is $3,815
(b) The amount owed At the end of 2 years is $4,158.35
Step-by-step explanation:
The given parameters on the loan amount are;
The amount Salma borrows = $3,500
The interest rate at which the loan is borrowed, r = 9% compound interest annually
The assumption are that no payments are made out of the loan
(a) The formula for finding a compound interest loan amount, 'A' is given as follows;
[tex]A = P\cdot \left(1 + \dfrac{r}{n} \right)^{n\cdot t}[/tex]
Where;
A = The amount owed
P = The principal (the initial amount borrowed)
r = The interest rate = 9% = 0.09
n = The number of times the interest is paid per unit period, 't' = 1
t = The number of periods of the loan = Number of years
At the end of 1 year, t = 1, we get;
[tex]A = 3,500 \times \left(1 + \dfrac{0.09}{1} \right)^{1 \times 1} = 3815[/tex]
The amount owed, A = $3,815 at the end of 1 year
(b) The amount owed at the end oy 2 years is found by plugging in t = 2 years into the formula for finding the amount owed by the borrower, therefore, we get;
[tex]A = 3,500 \times \left(1 + \dfrac{0.09}{1} \right)^{1 \times 2} = 4,158.35[/tex]
At the end of 2 years, the amount owed, A = $4,158.35
PLEASE HELP MEH I'M STRUGGLIN YmY
The construction of a tangent to a circle given a point outside the circle can be justified using the second corollary to the inscribed angle theorem. An alternative proof of this construction is shown below. Complete the proof.
fill up ALL the empty spaces
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Answer: I think you are asking for #2 = CD = AD
Explanation:
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:
hope this helps you.look it once.
Ay 31 YO METAL TOP School Factcoobrom sovin 9.6.PS-18 Question Help The circumference of the hub cap of a tire is 73.66 centimeters. Find the area of this hub cap. Use 3.14 for at. Use pencil and paper. If the circumference of the hub cap were smaller, explain how this would change the area of the hub cap. The area of this hub cap is about square centimeters. (Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All Check Answer Back Neats
Answer:
432 square centimeters
Step-by-step explanation:
Given :
The circumference of a hub cap is = 73.66 cm
The circumference of a circle is given as = 2πr, where r is the radius of the circular hubcap.
So , 2πr = 73.66
⇒ [tex]$r=\frac{73.66}{2 \times \pi}$[/tex]
⇒ [tex]$r=\frac{73.66}{2 \times 3.14}$[/tex] (Using, π = 3.14)
⇒ r = 11.73 cm
Therefore the area of the hub cap is given by A = [tex]$\pi r^2$[/tex]
A = [tex]$3.14 \times 11.73 \times 11.73$[/tex]
= 432 [tex]$cm^2$[/tex]
If the circumference of the hubcap were smaller, the area of the hubcap would be smaller too, since the circumference of the hubcap is proportional to the radius which is proportional to the area too.
If you can help, u r much appreciated : )))
I'm so sorry i wud help you but unfortunately I can't see the question fully!
Answer:
Is that all it tells you because I see no information to help answer the question
I see "month" and I see "Number of movie"
PLZ HELP ASAP. WILL GIVE BRAINLIEST IF CORRECT
What is the length of the unknown side of the right triangle using the Pythagorean Theorem?
7
24
25
31
Answer:
25 is the answer.
Step-by-step explanation:
Answer:
25 because 7 squared plus 24 squared is 625 then you find the square root which is 25.
PLEASE HELP WITH THISS.......
GF = ½ RT
Step-by-step explanation:
SG=GR (given)
SF=FT (given)
line GF is a midpoint in triangle RST, so it is therefore ½ the angle parallel to it(viz. RT)
The square root of 17 is between the what two whole numbers? (just list them with a comma in between them.)
Answer:
17 lies between 16 and 25. So√17 lies between √16 and √25. The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.
Answer:
The answer is 16,25
Which of these two kites we use more paper to make? Circle your answer?
Jamie Drew snowflake on graph paper. What is the area and square units?
Pleas do one or both of these and explain. I don't know how to do this and really need to know how!!
Answer:
I believe both kites use the same amount of paper
Step-by-step explanation:
They both have equal measures but I'm not too sure
Caden earn a total of $10 for two hours of yardwork. After join a total of three hours of yard work, how much money will Kayden have earned? Assume the relationship is directly proportional.
Answer:
$25
Step-by-step explanation:
Its $5 dollars for each hour so, the two hours together are $10. With the 3 hours Caden did, he earned $25.
Answer: 25
then Step-by-step explanation: if 10 divided by 2 is five, ( 5$ an hour) then just add three more fives i think
Write the equation in slope-intercept form.
8y - 3x = 16
Annita sat outside the grocery store selling cookbooks. She kept track of how many cookbooks she sold over a seven day period. She added the number of books sold each day to the previous day and plotted her results on the line graph shown. When rounded to the nearest whole number, which of the following is closest to the mean number of cookbooks Annita sold each day?
thx in advance for the help
Answer: [tex]x\geq 13[/tex]
Step-by-step explanation:
Given
The inequality is [tex]2x-7\geq 19[/tex]
adding both side 7
[tex]2x-7+7\geq 19+7\\2x\geq 26[/tex]
Multiply both sides by [tex]\frac{1}{2}[/tex]
[tex]\dfrac{1}{2}\times 2x\geq 26\times \dfrac{1}{2}\\\\x\geq 13[/tex]
the shaded region in the figure indicates the solution set.
. Government Waste In a Gallup poll 513 national adults aged 18 years or older who consider themselves to be Republican were asked, "Of every tax dollar that goes to the federal government in Washington, D.C., how many cents of each dollar would you say are wasted?" The mean wasted was found to be 54 cents with a standard deviation of 2.9 cents. The same question was asked of 513 national adults aged 18 years or older who consider themselves to be Democrat. The mean wasted was found to be 41 cents with a standard deviation of 2.6 cents. Construct a 95% confidence interval for the mean difference in government waste, mR - mD. Interpret the interval.
Answer:
Part A
The 95% confidence interval is approximately 12.66 ≤ [tex]m_R[/tex] - [tex]m_D[/tex] ≤ 13.34
Part B
We are 95% confident that the true difference in the mean amount of waste per dollar stated by the two categories of adults is larger than zero and it is approximately between 12.66 and 13.34
Step-by-step explanation:
Part A
The given parameters are;
The mean amount adults that consider themselves Republican say is wasted for every dollar, [tex]m_R[/tex] = 54 cents
The standard deviation of the statistics, s₁ = 2.9 cents
The number of respondents in the group, n₁ = 513
The mean amount adults that consider themselves Democrats say is wasted for every dollar, [tex]m_D[/tex] = 41 cents
The standard deviation of the statistics, s₂ = 2.6 cents
The number of respondents in the group, n₂ = 513
The F-test, F = s₁²/s₂² = 2.9²/2.6² = 1.244
The critical-t, t* = 1.962
F ≤ t*, therefore, we pool the data
[tex]s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]
[tex]s_p =\sqrt{\dfrac{\left ( 513-1 \right )\cdot 2.9^{2} +\left ( 513-1 \right )\cdot 2.6^{2}}{513+513-2}} = \sqrt{7.585}[/tex]
The 95% confidence interval is given by the following formula;
[tex]\left (m_R- m_D \right )\pm t^* \cdot s_p \cdot\sqrt{\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}}}[/tex]
The test statistic, is given as follows;
[tex]t = \dfrac{m_R - m_D}{s_p \times\sqrt{ \dfrac{1}{n_1} + \dfrac{1}{n_2}} }[/tex]
Therefore;
[tex]t = \dfrac{54 - 41}{\sqrt{7.585} \times\sqrt{ \dfrac{1}{513} + \dfrac{1}{513}} } \approx 75.598[/tex]
Given that the test statistic, t = 75.598 > The critical-t, t* = 1.962, we reject the null hypothesis, therefore, there is significant statistical evidence to suggest that there is a difference in the mean stated by the two sets
[tex]s_p =\sqrt{\dfrac{\left ( 513-1 \right )\cdot 2.9^{2} +\left ( 513-1 \right )\cdot 2.6^{2}}{513+513-2}} = \sqrt{7.585}[/tex]
[tex]C. I. = \left (54- 41 \right )\pm 1.962 \times \sqrt{7.585} \times \sqrt{\dfrac{1}{513}+\dfrac{1}{513}}[/tex]
The 95% confidence interval, C.I. ≈ 12.66 ≤ [tex]m_R[/tex] - [tex]m_D[/tex] ≤ 13.34
Part B
From the 95% confidence interval, we are 95% confident that the true difference in the mean amount adult who consider themselves Republicans say politicians waste and the true difference in the mean amount adult who consider themselves Democrats say politicians waste is between 12.66 and 13.34
Given that there is no '0' in the range of values in the 95% confidence for the difference in mean from the two groups, difference in the mean amount of waste per dollar observed by the two categories of adults.
Please answer both A. and B.
Thank you!
Answer: (b)-175 ft
Step-by-step explanation:
In [tex]\triangle ABC\ \text{and}\ \triangle CDE[/tex]
[tex]\angle ACB=\angle ECD\quad [\text{vertically opposite angles}]\\\angle ABC=\angle CDE\quad [\text{Each angle is }90^{\circ}]\\\therefore \triangle ABC \sim\ \triangle CDE\quad [\text{by AA similarity criteria}][/tex]
(ii)for similar triangles, we can write
[tex]\Rightarrow \dfrac{100}{d}=\dfrac{4x}{7x}\\\\\Rightarrow d=100\times \dfrac{7}{4}=175\ ft[/tex]
A right triangle and two of its side lengths are shown below which one of the following measurements is the length of the hypotenuse
Answer:
20 units
Step-by-step explanation:
By applying Pythagoras theorem in the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
(Hypotenuse)² = (12)² + (16)²
Hypotenuse = [tex]\sqrt{144+256}[/tex]
= [tex]\sqrt{400}[/tex]
= 20 inches
Therefore, measure of the hypotenuse of the given right triangles is 20 inches.
help me please. Very much appreciated
Answer:
A = 23.2 mm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 8 and h = 5.8 , then
A = 0.5 × 8 × 5.8 = 4 × 5.8 = 23.2 mm²
What are the solutions to the quadratic equation 2x2 - 8x-24 = 0?
A. X = -2 and x = 6
B. X=-3 and x = 8
C. X= -6 and x = 4
D. x= -4 and x = 6
Answer:
it is A . I hope its helpful
What type of polynomial is this
Answer:
trinomial..............
Find the mean of 9,5,10 graphically will mark Brainliest if correct ( no files or links)
Answer:
the answer to the question is 8
Is 0.5 meter high or low?
Please hurry:))!
Answer:
It depends what you are comparing that height to, but in general 0.5 meters is low.
Pls pls pls answer I need this done before 10;50
Answer:
1/12
Step-by-step explanation:
The answer choices are
∠3 ≅ ∠2
ℓ ∥ m
∠1 ≅ ∠2
∠1 ≅ ∠3
Answer:
∠1 ≅ ∠3
Step-by-step explanation:
What is given is literally in the picture.
Mel randomly selects a coin 150 times selecting a dime 30 times, the experimental probability is 1/5 what is the theoretical probability?
Answer:
Step-by-step explanation:
We can calculate probability by looking at the outcomes of an experiment or by reasoning What is the theoretical probability that a fair coin lands on heads? Choose 1 answer: Random numbers for experimental probability. This means that if we roll a die 60 times we can expect each of the six faces to come up.
Hope this helps.
Please give me brainliest if it is correct