Answer:
[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]
And we can use the normal standard distribution table and we got:
[tex] P(Z<-2.156) =0.0155[/tex]
Step-by-step explanation:
For this case we know the following info given:
[tex] p =0.14[/tex] represent the population proportion
[tex] n = 622[/tex] represent the sample size selected
We want to find the following proportion:
[tex] P(\hat p <0.11)[/tex]
For this case we can use the normal approximation since we have the following conditions:
i) np = 622*0.14 = 87.08>10
ii) n(1-p) = 622*(1-0.14) =534.92>10
The distribution for the sample proportion would be given by:
[tex] \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p}= 0.14[/tex]
And the deviation:
[tex]\sigma_{\hat p}= \sqrt{\frac{0.14*(1-0.14)}{622}}= 0.0139[/tex]
We can use the z score formula given by:
[tex] z=\frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And replacing we got:
[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]
And we can use the normal standard distribution table and we got:
[tex] P(Z<-2.156) =0.0155[/tex]
A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is: DD = 2.69 + 0.0138D.
1. What is the slope of the regression line?
2. Explain in specfic language what this slope says about this penguin's dives.
A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
B. If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent under water.
C. If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent under water.
3. According to the regression line, how long does a typical dive to a depth of 200 meters last?
4. According to the regression line, how long does a typical dive to a depth of 210 meters last?
5. According to the regression line, how long does a typical dive to a depth of 220 meters last?
6. According to the regression line, how long does a typical dive to a depth of 230 meters last?
7. According to the regression line, how long does a typical dive to a depth of 240 meters last?
8. According to the regression line, how long does a typical dive to a depth of 150 meters last?
9. According to the regression line, how long does a typical dive to a depth of 160 meters last?
10. According to the regression line, how long does a typical dive to a depth of 170 meters last?
11. According to the regression line, how long does a typical dive to a depth of 180 meters last?
12. According to the regression line, how long does a typical dive to a depth of 190 meters last?
Answer:
(1)0.0138
(2)A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
Nos 3-12: See Explanation
Step-by-step explanation:
Given the regression equation for the relation of dive duration (DD) to depth (D).
[tex]DD = 2.69 + 0.0138D\\$Where: Duration DD is measured in minutes\\epth D is in meters.[/tex]
(1)The slope of the regression lie =0.0138
(2)
When D=1, DD = 2.69 + 0.0138(1)=2.7038
When D=2, DD = 2.69 + 0.0138(2)=2.7176
2.7176-2.7038=0.0138
Therefore, If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
(3) When depth, D =200 meters
DD = 2.69 + 0.0138(200)=5.45 Minutes
(4) When depth, D =210 meters
DD = 2.69 + 0.0138(210)=5.588 Minutes
(5) When depth, D =220 meters
DD = 2.69 + 0.0138(220)=5.726 Minutes
(6) When depth, D =230 meters
DD = 2.69 + 0.0138(230)=5.864 Minutes
(7) When depth, D =240 meters
DD = 2.69 + 0.0138(240)=6.002 Minutes
(8) When depth, D =150 meters
DD = 2.69 + 0.0138(150)=4.76 Minutes
(9) When depth, D =160 meters
DD = 2.69 + 0.0138(160)=4.898 Minutes
(10) When depth, D =170 meters
DD = 2.69 + 0.0138(170)=5.036 Minutes
(11) When depth, D =180 meters
DD = 2.69 + 0.0138(180)=5.174 Minutes
(12) When depth, D =190 meters
DD = 2.69 + 0.0138(190)=5.312 Minutes
A regression line is only a single line that fits the data the best. It tells how steep it is, whereas the intercept reveals where it intersects an axis.
Regression line:For question 1):
By calculating the slope of the regression line we get the slope value that is [tex]= 0.0138[/tex]
For question 2):
Describe whatever this slope means about this penguin's dives in precise terms.
The time spent under liquid increases by 0.0138 minutes whenever the diving depth is raised by one meter, which is equal to "Option A".
For question 3):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times200 = 2.69+2.76 = 5.45\ minutes[/tex]
For question 4):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times210 = 2.69 + 2.898 = 5.588\ minutes[/tex]
For question 5):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 220 = 2.69 + 3.036 = 5.726\ minutes[/tex]
For question 6):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times230 = 2.69 + 3.174 = 5.864 \ minutes[/tex]
For question 7):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times240 = 2.69 + 3.312 = 6.002\ minutes[/tex]
For question 8):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 150 = 2.69 + 2.07 = 4.76\ minutes[/tex]
For question 9):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 160 = 2.69 + 2.208 = 4.898\ minutes[/tex]
For question 10):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 170 = 2.69 + 2.346 = 5.036\ minutes[/tex]
For question 11):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 180 = 2.69 + 2.484 = 5.174 \ minutes[/tex]
For question 12):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 190 = 2.69 + 2.622 = 5.312\ minutes[/tex]
Find out more about the regression line here:
brainly.com/question/7656407
if F (x) equals 4x + 7 which of the following is the inverse of F(x)
Answer:
[tex]F^{-1}(x)=\dfrac{x-7}{4}[/tex]
Step-by-step explanation:
To find the inverse function, solve for y the relation ...
F(y) = x
4y +7 = x
4y = x - 7
y = (x -7)/4 . . . . the inverse function
[tex]\boxed{F^{-1}(x)=\dfrac{x-7}{4}}[/tex]
which expression is equivalent to (x6y8)3/x2y2
Answer:
[tex]x^{16}y^{22}[/tex]
Step-by-step explanation:
[tex]\frac{(x^{6}y^{8}) ^{3}}{x^{2}y^{2}}=\\\\x^{16}y^{22}[/tex]
Hope this helps!
An equilateral triangle have always _________ vertex and _______ lines of symmetry.
a) (3 , 1)
b) ( 4, 0)
c) (3 , 3 )
d) (3, 2 )
Answer:
hey mate,
here is your answer. Hope it helps you.
C-(3,3)
Step-by-step explanation:
An equilateral triangle, which has three equal sides, has three lines of symmetry. This is because you can fold an equilateral triangle in three halves and the are equal. Hence an equilataral triangle has three vertices and 3 lines of symmetry.
A hot dog has about 1/4 the amount of protein as 3 ounces of hamburger. Together, they have about 25 grams of protein. How many grams of protein are in a 3 oz hamburger?
Answer:
(1) protein in hot dog = ¼ * protein in 3 ounces of hamburger
(2) protein in hot dog + protein in 3 ounces of hamburger = 25
So we need to re-arrange (1) and (2) to solve for the protein in 3 ounces of hamburger!
(re-arrange (1)): 4 * protein in hot dog = protein in 3 ounces of hamburger
(re-arrange (2)): protein in hot dog = 25 - protein in 3 ounces of hamburger
(plugging re-arranged (2) into re-arranged (1)):
4 * (25 - protein in 3 ounces of hamburger) = protein in 3 ounces of hamburger ( multiplying )
100- 4 protein in 3 ounces of hamburger = protein in 3 ounces of hamburger
solving for the protein in 3 ounces of hamburger:
5 * protein in 3 ounces of hamburger = 100
protein in 3 ounces of hamburger = 20 gram
From a barrel of colored marbles, you randomly select 1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles. Find the experimental probability of randomly selecting a marble that is NOT yellow.
A: 8/9
B: 9/10
C: 11/18
D: 7/9
Answer:
8/9
Step-by-step explanation:
1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles = 18 marbles
The number that are not yellow = total - yellow
P( not yellow) = number that are not yellow / total
= (18-2) / 18
= 16/18
=8/9
Can someone please help me fast
Answer:
x = 3.5
Step-by-step explanation:
Since the triangles are similar we can use ratios to solve
4 7
------ = ------
(4+2) ( 7+x)
Using cross products
4(7+x) = 7*(4+2)
Distribute
28+4x = 42
Subtract 28 from each side
4x = 42-28
4x= 14
Divide by 4
4x/4 = 14/4
x = 7/2
Venera sent a chain letter to her friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of
people, P(t), who receive the email is modeled by the following function:
3t+7
P(t) = 2
Complete the following sentence about the monthly rate of change in the number of people who receive
the email.
Round your answer to two decimal places.
Every month, the number of people who receive the email is multiplied by a factor of
Answer:
It is multiplied by a factor of 8
Step-by-step explanation:
Every month, the number of people who receive the email is multiplied by a factor of 8.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
Venera sent a chain letter to her friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in months, since Venera sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:
[tex]\rm P(t) = 2^{3t+7}[/tex]
Every month, the number of people who receive the email is multiplied by a factor will be
For t = 2, we have
P(2) = 2³⁽²⁾⁺⁷
P(2) = 2¹³
For t = 3, we have
P(3) = 2³⁽³⁾⁺⁷
P(3) = 2¹⁶
Then the factor will be
⇒ P(3) / P(2)
⇒ 2¹⁶ / 2¹³
⇒ 2³
⇒ 8
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ2
Mrs. Fields needs more chocolate chips to make cookies. The store has bags that weigh 0.45 lbs., 0.434 lbs., and 0.4 lbs. Which bag should she purchase if she wants the most chocolate chips?
Answer:
bag weigh 0.45 lbs
Step-by-step explanation:
What is the volume of a rectangular prism with a length of 12ft, a width of 10ft, and a height of 18ft?
Answer:
2160ft³
Step-by-step explanation:
V=whl=10·18·12=2160ft³
Jamie needs the following items from the hardware store a drill bit that cost 4.99 nails that caused 0.46 and sandpaper that cost 0.89 how much money was spent if the sales tax rate is 6%
Answer: $5.96
Step-by-step explanation:
4.99 + 0.46 + 0.89 is what she paid, not with tax. That equals 6.34.
Applying 6% means we calculate 6% of 6.34 and then subtract it from 6.34. (Or, we can also calculate 100-6%=94% of 6.34). Either way, the answer is 5.9596, or rounded, 5.96.
Hope that helped,
-sirswagger21
Which cosine function has maximum of 0.5, a minimum of -0.5, and a period of 2(pi)/3
Answer:
The answer is "[tex]\bold{y=0.5 \cos 3 \theta}[/tex]"
Step-by-step explanation:
The choices were missing the question so the answer to this question can be defined as follows:
The answer is [tex]y= 0.5 \cos 3\theta[/tex] because:
[tex]\Rightarrow -1 \leq \cos 3 \theta \leq 1\\\\\Rightarrow -0.5 \leq \cos 3 \theta \leq 0.5\\[/tex]
So, the maximum value is = 0.5 and the minimum value is = -0.5 of [tex]\frac{2\pi}{3}[/tex].
Answer:
D. y= 0.5 cos 3 theta
Step-by-step explanation:
Find five consecutive integers such that the sum of the first and 5 times the third is equal to 41 less than 3 times the sum of the second fourth and fifth
Answer:
see below
Step-by-step explanation:
We'll cal the first integer x and then the rest of them will be x + 1, x + 2, x + 3 and x + 4. We can write x + 5(x + 2) = 3(x + 1 + x + 3 + x + 4) - 41.
x + 5x + 10 = 3(3x + 8) - 41
6x + 10 = 9x + 24 - 41
6x + 10 = 9x - 17
3x = 27
x = 9
The numbers are 9, 10, 11, 12, 13.
Jacob put his 731 Marbles and 37 bags if he puts the same amount in each bag how many marbles were in each bag how many marbles were left out of the backs
Answer:
19 marbles in each bag 28 left over
Step-by-step explanation:
the first step to this problem is to find out the number of marbles in each bag.
if there were 731 marbles and 37 bags, we need to divide 731 by 37.
731/37 = 19[tex]\frac{28}{37}[/tex]
therefore there are 19 marbles in each bag.
the second part of the question is to determine how many are left out or in other words how many numbers are "left over"
since the fraction is 28/37 there are 28 marbles that are left out of the bag.
feel free to ask questions, hope this helped you!
A survey taken in a large statistics class contained the question: "What's the fastest you have driven a car (in miles per hour)?" The five-number summary for the 87 males surveyed is: min = 55, Q1 = 95, Median = 110, Q3 = 120, Max = 155 Should the largest observation in this data set be classified as an outlier? No Yes
Answer:
NO
Step-by-step explanation:
To find out which observation to classify as an outlier, whether the largest or not, a very good approach or way to do this is to apply the 1.5(IQR) rule.
According to the rule, for finding the largest observation in the data that can be classified as an outlier, we would use the formula = Q3 + 1.5(IQR).
Q3 = 120
IQR = Q3 - Q1 = 120 - 95 = 25
Lets's plug these values into Q3 + 1.5(IQR)
We have,
120 + 1.5(25)
= 157.5
Since our max in the observation is given as 155, the largest observation in the data set cannot be set as an outlier because 157.5 which we got from our calculation is higher than the max value we have in the data set.
Our answer is NO.
However, the smallest observation should be set as outlier because:
Q1 - 1.5(IQR) = 95 - (1.5*25) = 57.5, which gives us an outlier that falls within our data range.
Cheeseburgers to go has advertised for counter help. If you take the job, you will be working 18 hours
a week for $69.20 per week. How much would you make an hour?
Answer:
about $3.84
Step-by-step explanation:
you do 69.20 divided by 18
Assuming that a cheese sandwich consists of 2 slices of bread and 3 slices of cheese, determine the number of whole cheese sandwiches that can be prepared from 32 slices of bread and 51 slices of cheese. g
Answer:
Only 16 whole sandwiches can be produced
Step-by-step explanation:
From the question, we know that we will need two slices of bread to make a full sandwich.
We can divide the number of slices of bread by two to check how many full sandwiches can be made.
Number of complete sets of bread = 32/2 = 16 sets
Similarly, we can divide the number of slices of cheese by 3 to find out the number of complete sets of cheese that will be there:
Number of complete sets of cheese = 51/3 = 17 sets
Since we have more cheese than bread, the number of whole sandwiches that can be made will be limited to the number of sets of bread available. (in this case, the ingredient smaller in quantity will be used to limit the production) which is = 16
Therefore only 16 whole sandwiches can be produced
Explain why the sum of the angle measures in any
triangle is 180º.
Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360
hope this helped
Sandy is tiling her floor woth square tiles.The kength one of the sides of each tiles is3/4 foot.Her floor is 9 feet by 10 feet .What is the area of the tile she using to tile her floor
Hey there! I'm happy to help!
Since the tiles are square, all of their sides are the same. We see that one of the side lengths is 3/4. So, to find the area of the square, we square 3/4 (multiply it by itself)
3/4 × 3/4= 9/16
Therefore, the area of Sandy's tile is 9/16 square feet.
BONUS
We can also find the area of our floor, which is 9 feet by 10 feet, so it is 90. We can then divide by 9/16 to figure out how many tiles we need.
90/9/16=160
So, you would need 160 of these tiles to fill the floor.
I hope that this helps!
write down the exact value of
a. cos 30 degrees
b. sin45 degrees
c. tan 30 degrees
Answer:
.86602 a
.707106 b
.577355 c
Step-by-step explanation:
entered itno calculator
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 The test statistic to test the null hypothesis equals _____.
Answer:
The test statistic to test the null hypothesis equals 1.059
Step-by-step explanation:
From the given information; we have:
Treatment Observations
A 20 30 25 33
B 22 26 20 28
C 40 30 28 22
The objective is to find the test statistic to test the null hypothesis; in order to do that;we must first run through a series of some activities.
Let first compute the sum of the square;
Total sum of squares (TSS) = Treatment sum of squares [tex](T_r SS)[/tex] + Error sum of squares (ESS)
where:
(TSS) = [tex]\sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}oo)^2[/tex] with (n-1) df
[tex](T_r SS)[/tex] [tex]= \sum \limits ^v_{i=1} n_i( \overline yio- \overline {y}oo)^2[/tex] with (v-1) df
[tex](ESS) = \sum \limits ^v_{i=1} \sum \limits ^{n_i}_{j-1}(yij- \overline {y}io)^2[/tex] with (n-v) df
where;
v= 3
[tex]n_i=[/tex]4
i = 1,2,3
n =12
[tex]y_{ij}[/tex] is the [tex]j^{th[/tex] observation for the [tex]i^{th[/tex] treatment
[tex]\overline{y}io[/tex] is the mean of the [tex]i^{th[/tex] treatment i = 1,2,3 ; j = 1,2,3,4
[tex]\overline y oo[/tex] is the overall mean
From the given data
[tex]\overline y oo = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij)^2= 27[/tex]
[tex]TSS = \dfrac{1}{12} \sum \limits ^3_{i=1} \sum \limits ^{4}_{j=1}(yij- 27)^2 = 378[/tex]
[tex]T_r SS= \sum \limits^3_{i=1}4 (\overline y io - \overline yoo)^2[/tex]
[tex]=4(27-27)^2+4(24-27)^2+4(30-27)^2 = 72[/tex]
Total sum of squares (TSS) = Treatment sum of squares [tex](T_r SS)[/tex] + Error sum of squares (ESS)
(TSS) = 378 - 72
(TSS) = 306
Now; to the mean square between treatments (MSTR); we use the formula:
MSTR = TrSS/df(TrSS)
MSTR = 72/(3 - 1)
MSTR = 72/2
MSTR = 36
The mean square within treatments (MSE) is:
MSE = ESS/df(ESS)
MSE = 306/(12-3)
MSE = 306/(9)
MSE = 34
The test statistic to test the null hypothesis is :
[tex]T = \dfrac{ \dfrac{TrSS}{\sigma^2}/(v-1) }{ \dfrac{ESS}{\sigma^2}/(n-v) } = \dfrac{MSTR}{MSE} \ \ \ \approx \ \ T(\overline {v-1}, \overline {n-v})[/tex]
[tex]T = \dfrac{36}{34}[/tex]
T = 1.059
what two numbers add to -7 and multiply to -60
Answer:
The answer would be 5 and -12
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.
x4 + x ? 7 = 0, (1, 2)
f(x) = x4 + x ? 7
is (FILL IN)
a) defined
b) continuous
c) negative
d) positive on the closed interval [1, 2],
f(1) = ?? FILL IN , and f(2) = ?? FILL IN
Since ?5 < FILL IN a)? b)? c)? d)0 < 11, there is a number c in (1, 2) such that
f(c) = FILL IN a)? b)? c)0 d)11 e)-5
by the Intermediate Value Theorem. Thus, there is a FILL IN a) limit b)root c) discontinuity of the equation
x4 + x ? 7 = 0
in the interval (1, 2).
Answer:
The correct option is d
[tex]f(1) = -5[/tex]
[tex]f(2) = 11[/tex]
The correct option is d
The correct option is c
the correct option is b
Step-by-step explanation:
The given equation is
[tex]f(x) = x^4 + x -7 =0[/tex]
The give interval is [tex](1,2)[/tex]
Now differentiating the equation
[tex]f'(x) = 4x^3 +7 > 0[/tex]
Therefore the equation is positive at the given interval
Now at x= 1
[tex]f(1) = (1)^4 + 1 -7 =-5[/tex]
Now at x= 2
[tex]f(2) = (2)^4 + 2 -7 =11[/tex]
Now at the interval (1,2)
[tex]f(1) < 0 < f(2)[/tex]
i.e
[tex]-5 < 0 < 11[/tex]
this tell us that there is a value z within 1,2 and
f(z) = 0
Which implies that there is a root within (1,2) according to the intermediate value theorem
in a survey of more than 3000 people 93% of the respondents claimed to prefer Isaac's immaculate ice cream over any other brand of ice cream. which of the folloling groups were surveyed.
Answer:
The answer is 2,790.
Step-by-step explanation:
Here's a handy tool.
93% of 1 = 0.93 93% of 131 = 121.83 93% of 261 = 242.73 93% of 391 = 363.63
93% of 2 = 1.86 93% of 132 = 122.76 93% of 262 = 243.66 93% of 392 = 364.56
93% of 3 = 2.79 93% of 133 = 123.69 93% of 263 = 244.59 93% of 393 = 365.49
93% of 4 = 3.72 93% of 134 = 124.62 93% of 264 = 245.52 93% of 394 = 366.42
93% of 5 = 4.65 93% of 135 = 125.55 93% of 265 = 246.45 93% of 395 = 367.35
93% of 6 = 5.58 93% of 136 = 126.48 93% of 266 = 247.38 93% of 396 = 368.28
93% of 7 = 6.51 93% of 137 = 127.41 93% of 267 = 248.31 93% of 397 = 369.21
93% of 8 = 7.44 93% of 138 = 128.34 93% of 268 = 249.24 93% of 398 = 370.14
93% of 9 = 8.37 93% of 139 = 129.27 93% of 269 = 250.17 93% of 399 = 371.07
93% of 10 = 9.30 93% of 140 = 130.20 93% of 270 = 251.10 93% of 400 = 372.00
Write the quotient in simplest form. Type answer as integer or a fraction
Answer:
[tex]-\dfrac{1}{26}[/tex]
Step-by-step explanation:
[tex]-\dfrac{12}{13}\div 24=\\\\-\dfrac{12}{13} \times \dfrac{1}{24}=\\\\-\dfrac{12}{13\times 24}=\\\\-\dfrac{1}{26}[/tex]
Hope this helps!
Can someone please help me
Answer:
6
Step-by-step explanation:
Similar triangles. MNE is ABC but 3/4 the size. Multiply each side by 3/4 to get lengths.
x = 8 *3/4 = 6
Please help me with this question!!!
Answer:
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
Step-by-step explanation:
Using Euler's formula, this can be written as ...
x^2 = 9·e^(i5π/6)
Then the square roots are ...
x = (±√9)e^((i5π/6)/2) = ±3e^(i5π/12)
Of course, multiplying by -1 is the same as adding 180° to the angle.
The square roots are ...
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
A credit card had an APR of 15.98% all of last year, and compounded interest daily. What was the credit card's effective interest rate last year?
A.
17.32%
B.
17.20%
C.
16.96%
D.
16.62%
Answer:
Option(B) is the correct answer to the given question.
Step by Step Explanation
We know that
[tex]A\ =\ P \ *(\ 1+\ \frac{r}{n} \ ) ^{nt}[/tex]
Here A=amount
r=15.98%=0.1598
n=365
t=1
Putting these values into the equation
[tex]A\ =\ P \ *(\ 1+\ \frac{0.1598}{365} \ ) ^{365}[/tex]
[tex]A\ =\ P \ *(\ 1+\ 0.000437) ^\ { 365}[/tex]
[tex]A\ =\ P \ *(\ 1.000437 ) ^{365}[/tex]
[tex]A\ =1.17288 P[/tex]
Now we find the interest
I=[tex]1.17288P\ -P\\=\ 0.17288P\\\ ~ 0.1720P[/tex]
Therefore effective interest rate of the last year can be determined by
[tex]\frac{0.1720P}{P}[/tex]
=0.1720 *100
=17.20%
Answer:
17.32%
Step-by-step explanation:
If log a = x and log b = y, then log (ab2) equals
1
1.
2 (x +y)
1
2.
x + 2 y
x + 2y
3
4.
2x + 2y
Su
uid Toolhar
Answer:
The answer for log(ab²) is x + 2y.
Step-by-step explanation:
You have to apply Logarithm Law,
[tex] log(a) + log(b) \: ⇒ \: log(a \times b) [/tex]
[tex] log( {a}^{n} ) \: ⇒ \: n log(a) [/tex]
In this question, you have to seperate it out :
[tex] log(a {b}^{2} ) = log(a) + log( {b}^{2} ) [/tex]
[tex] log( {b}^{2} ) = 2 log(b) [/tex]
[tex]let \: log(a) = x[/tex]
[tex]let log(b) = y[/tex]
[tex] log(a {b}^{2} ) = log(a) + 2 log(b) [/tex]
[tex] log(a {b}^{2} ) = x + 2y[/tex]
What is the height of a sphere of radius 6 inches?
Answer:
12 inches.
Step-by-step explanation:
The height of a sphere = the length of its diameter.
Diameter = 2 * radius = 12 ins.
