The rate of growth in the exponential function is 1.98%
Exponential FunctionAn exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
To solve this problem, we have to model the growth in an exponential function.
Population in 1997 = 2.12 million
Population in 2006 = 2.53 million
Time = 9
Since this is an exponential growth function, we can write this as;
2.53 = 2.12(1 + r)⁹
where r = rate of growth
2.53 = 2.12(1 + r)⁹
r = 0.0198
r = 1.98%
The rate of growth is 1.98%
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Need help asap!! What is the circumference of the circle shown?
Answer:
56.5
Step-by-step explanation:
Circumference = \(\pi d\)
C = 3.14(18) = 56.52
The Perimeter of Rhombus WXYZ is 240 cm and XY = 5k + 10
What is the value of'k?
w
х
A +
(B) 9
(С 10
[7 7
(D2
E 16
Z
A number is picked randomly in the range [0,7]. What is the probability that the number picked is between 3 and 5? What is the probability that the number picked is less than 4 knowing that the number usually picked appears to be in in the range [3,5]?
Answer:
(1) 0.125
(2) 0.125
Step-by-step explanation:
The total number of possible outcomes is:
N = 8
(1)
Compute the probability that the number picked is between 3 and 5 as follows:
Number of Favorable outcomes = 1
The probability is:
P (Number picked is between 3 and 5) = 1/8 = 0.125
Thus, the probability that the number picked is between 3 and 5 is 0.125.
(2)
The number usually picked appears to be in in the range [3,5], i.e. the numbers could be, {3, 4 or 5}.
Number of Favorable outcomes = n (Number < 4 and within [3, 5]) = 1
P (less than 4 ∩ within [3, 5]) = 1/8 = 0.125
Thus, the probability that the number picked is less than 4 knowing that the number usually picked appears to be in in the range [3,5] is 0.125.
find the product in lowest terms 24/18x2/17x34/3
Answer:
Step-by-step explanation:
To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:
(24/18) * (2/17) * (34/3)
First, we can simplify the fractions by reducing any common factors in the numerators and denominators:
24/18 = (212)/(29) = 12/9 = 4/3
2/17 = 2/17
34/3 = (2*17)/3 = 34/3
Now we can multiply the simplified fractions:
(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153
The product of the given fractions in lowest terms is 272/153.
There are 6 acts in a talent show.
An acrobat, a dancer, a guitarist, a singer, a violinist, and a whistler.
A talent show host randomly schedules the 6 acts.
Compute the probability of each of the following events.
Event A: The acrobat is first, the singer is second, the violinist is third, and the whistler is fourth.
Event B: The first four acts are the whistler, the acrobat, the guitarist, and the dancer, In any order.
Write your answers as fractions in simplest form.
P(A) =
P (B) =
The probability of Event A is 1/360 and the probability of Event B is 1/15.
For Event A, we can calculate the probability by considering the order in which the acts are scheduled.
There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.
Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.
Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.
Therefore, the total number of possible ways to schedule all 6 acts is:
6 x 5 x 4 x 3 x 2 x 1 = 720
Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.
There are 2 remaining acts, so there are 2 possible choices for the fifth act.
Only one act remains for the last slot.
Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:
1 x 1 x 1 x 1 x 2 x 1 = 2
Thus, the probability of Event A is:
P(A) = 2/720 = 1/360
For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.
There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.
Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.
Therefore, the total number of possible ways to schedule the first four acts is:
4 x 3 x 2 x 1 = 24
Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.
Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:
24 x 2 = 48
Thus, the probability of Event B is:
P(B) = 48/720 = 1/15
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3. Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years. Calculate a 96% CI on the death rate from lung cancer.
Answer:
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).
Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.
This means that \(n = 1000, \pi = \frac{450}{1000} = 0.45\)
96% confidence level
So \(\alpha = 0.04\), z is the value of Z that has a p-value of \(1 - \frac{0.04}{2} = 0.98\), so \(Z = 2.054\).
The lower limit of this interval is:
\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177\)
The upper limit of this interval is:
\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823\)
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
Find the area of the yellow region. Round to the nearest tenth. 7.53cm
The figure shows a square inscribed in a circle of radius r = 7.53 cm.
The yellow region corresponds to the area of the circle minus the area of the square.
The area of a circle of radius r is:
\(A_c=\pi r^2\)Calculating:
\(A_c=\pi(7.53\text{ cm})^2=178.13\text{ }cm^2\)The radius of the circle is half the diagonal of the square. The diagonal of the square is:
d = 2 x 7.53 cm = 15.06 cm
The area of a square, given the diagonal d, is calculated as follows:
\(A_s=\frac{d^2}{2}\)Calculating:
\(\begin{gathered} A_s=\frac{(15.06\text{ cm})^2}{2} \\ \\ A_s=113.40\text{ }cm^2 \end{gathered}\)The required area is:
A = 178.13 - 113.40 = 64.73 square cm
Polygon ABCD is drawn with vertices A(−4, −4), B(−4, −6), C(−1, −6), D(−1, −4). Determine the image coordinates of B′ if the preimage is reflected across y = 3.
B′(−4, 6)
B′(−4, 12)
B′(−1, −3)
B′(10, −6)
HELP PLEASE FAST
Find the second differences for the relation.
The second differences for the relation is -2 which is option A.
What is the second differences for the relation?To find the second differences, we need to calculate the difference between consecutive differences of the 'y' values in the given relation.
First, let's calculate the first differences:
-9 - (-4) = -5
-4 - (-1) = -3
-1 - 0 = -1
0 - (-1) = 1
-1 - (-4) = 3
-4 - (-9) = 5
Now, let's calculate the second differences:
-5 - (-3) = -2
-3 - (-1) = -2
-1 - 1 = -2
1 - 3 = -2
3 - 5 = -2
The second differences for the given relation are all -2.
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sequence three missing terms to comple 7444> →→19-
To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.
Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.
To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406
To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.
To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.
Therefore, the completed sequence is:
7444> →→19- → -7406 → -14831 → -22256
Each term in the sequence is obtained by subtracting 7425 from the previous term.
It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.
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Adalyn used 2.5 yards of fabric to make 3 decorative pillows. If she makes 12 pillows, how many yards of fabric will she need?
Answer:
Step-by-step explanation:
if Adalyn use 2.5 yards to make 3 pillows
than for 12 pillows she will use (2.5yards x12)/3=10 yards
you can see it with a different approach as well
2.5 y............3 pillows
5 yards.........6 pillows
7.5 yards.......9 pillows
10 yards............12 pillows
Find the mean, median, and mode of the data, if possible. f any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below
11.3 10.6 11.7 9.7 11.7 9.5 11.7
What is the mean score? Select the correct choice below and fill in any answer box to complete your choice
A. The mean score is Round to one decimal place as needed.)
B. There is no mean score. Does the mean represent the center of the data?
A. The mean represents the center
B. The mean does not represent the center because it is the smallest data value.
C. The mean does not represent the center because it is not a data value.
D. The mean does not represent the center because it is the largest data value.
What is the median score? Select the correct choice below and fill in any answer box to complete your choice.
A. The median score is 0
B. There is no median score.
Does the median represent the center of the data? (Round to one decimal place as needed.)
A. The median represents the center.
B. The median does not represent the center because it is not a data value. °
C. The median does not represent the center because it is the largest data value.
D. The median does not represent the center because it is the smallest data value.
What is the mode of the scores? Select the correct choice below and fill in any answer box to complete your choice
A. The mode(s) of the scores is (are)
B. There is no mode. Does (Do) the mode(s) represent the center of the data?
(Use a comma to separate answers as needed.)
A. The mode(s) represent(s) the center
B. The mode(s) can't represent the center because it (they) is (are) not a data value.
C. The mode(s) does (do) not represent the center because it (one) is the largest data value.
D. The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Answer:
Step-by-step explanation:
Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.
Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7
Mean = 76.2/7
Mean = 10.9
The mean score is 10.9 to 1 decimal place.
Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.
b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;
9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7
After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.
The median represents the center
c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.
The mode(s) does (do) not represent the center because it (one) is the largest data value.
given that y various with x, find the equation of direct variation when x=11 and y=14
Answer:
The equation of direct variation relates two variables that vary proportionally to each other, and can be written as y = kx, where k is the constant of proportionality. To find k, we can plug in the values of x and y given in the problem and solve for k:
y = kx
14 = k(11)
k = 14/11
Now that we know k, we can write the equation of direct variation as:
y = (14/11)x
Therefore, when x = 11 and y = 14, the equation of direct variation is y = (14/11)(11) = 14.
Which of the following equations correctly describes the graphed line?y = -1/2x - 5y = -1/2x + 5y = 1/2x + 5y = 1/2x - 5
We can see in the graph that the y-intercept is equal to +5. According to that, the correct options could be second and third options.
The line has a positive slope and the third option has a positive slope (1/2), therefore, this is the correct answer. (Since the second option has a negative slope (-1/2)).
The answer is y= 1/2x + 5
How do I find the value
A = 139°
B = 139°
You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.
The angle around a point always add up to 360°, so add the 41° angles.
41 + 41 = 82°
Then minus this by 360°.
360 - 82 = 278°
And to work out one angle, which gives you the angle for both, divide 278 by two.
278 ÷ 2 = 139°
Both A and B have an angle of 139°
Example:
To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:
3x - 5 = -2x + 7
5x = 12
x = 12/5
Then, plug x = 12/5 into either equation and solve for y:
y = 3(12/5) - 5
y = 36/5 - 25/5
y = 11/5
Therefore, the point of intersection is (12/5, 11/5).
If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:
slope = tan(41 degrees) ≈ 0.87
y = mx + b
y = 0.87x + 0
Then, you can use the same method as before to find the point of intersection with another line.
_______________________________________________________
The answer is 139 degrees, using the method I gave.
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A 3-column table with 4 rows. Column 1 has entries Computer repair, sales tax, gratuity, shipping. Column 2 is labeled Store A with entries 1,200 dollars, 6 percent, 15 percent, Free. Column 3 is labeled Store B with entries 1,350 dollars, 7 percent, 15 percent, 2 percent of total price.
How much sales tax will be charged at Store B?
Answer:
72 on edge
Step-by-step explanation:
Answer:
94.50
Step-by-step explanation:
2x-1=y
3x-1=y
Consider the system of equations above. Which of the following statements about this system is true?
Answer:
B; There is only one (x,y) solution and y is negative
Step-by-step explanation:
First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.
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There are 3/4 kilograms of salt in the jar Ms.Hernandez used 1/3 of the salt when she was making lunch how much salt did she use
Answer:
sd
Step-by-step explanation:
PLEASEEEE HELPP MEEE WITHHH NUMBERSSS 9 AND 10
PLEASEEE HELPPP MEEEEE!!!!!!!!
Answer:
9: 89°
Step-by-step explanation:
Inside of a triangle is 180, so 180-39-52=89
I'm sorry I can't answer 10 for you
5(10v-8w+4) as a distributive property
Using distributive property, the solution to the given expression is: 50v - 40w + 20
How to use distributive property?The Distributive Property is a term which is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.
For example:
4(3 + 5)
According to the distributive property, you first have to multiply out the bracket to get:
4*3 + 4*5 = 12 + 20
= 32
Thus:
5(10v - 8w + 4) = (5 * 10v) - (5 * 8w) + (5 * 4)
= 50v - 40w + 20
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given tan A=11/60 and that angle A is in quadrant 1, find the exact value of cos A in simplest form using a rational denominator
Answer:
\(\cos(A) = \frac{60}{61}\)
Step-by-step explanation:
Given
\(\tan(A) = \frac{11}{60}\)
\(0 \le A \le 90\) --- First Quadrant
Required
Find cos(A)
The tan of an angle is:
\(\tan(A) = \frac{Opposite}{Adjacent}\)
and
\(\tan(A) = \frac{11}{60}\)
By comparison:
\(Opposite = 11\)
\(Adjacent = 60\)
So, the hypotenuse is:
\(Hypotenuse^2 = Adjacent^2 + Opposite^2\)
\(Hypotenuse^2 = 60^2 + 11^2\)
\(Hypotenuse^2 = 3721\)
Take square roots
\(Hypotenuse = \sqrt{3721\)
\(Hypotenuse = 61\)
The cosine of an angle is:
\(\cos(A) = \frac{Adjacent}{Hypotenuse}\)
This gives:
\(\cos(A) = \frac{60}{61}\)
Question 2 The current report quantitatively analyzes three variables - load factors, revenue passenger mile, and available seat miles for American Airlines. The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics, focusing on domestic flights from January 2006 to December 2012. The quantitative analysis focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. Table 2: Summary Statistics of American Airlines (Domestic) Revenue Passenger Miles Mean 6,624,897 Median 6,522,230 Mode NONE Minimum 5,208,159 Maximum 8,277,155 Standard Dev 720,158.571 Variance 518,628,367,282.42 Load Factors Mean 82.934 Median 83.355 Mode 84.56 Minimum 74.91 Maximum 89.94 Standard Dev 3.972 Variance 15.762 Revenue Passenger Miles 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 0 10 American Airlines (Domestic) Performance 20 30 ● Revenue Passenger Miles 40 50 Load Factors Available Seat Miles 60 Mean 7,984,735 Median 7,753,372 Mode NONE Minimum 6,734,620 Maximum 9,424,489 Standard Dev 744,469.8849 Variance 554,235,409,510.06 70 80 Linear (Revenue Passenger Miles) 90 100 Figure 1: American Airlines (Domestic) Performance Write a report based on the given data. Please include additional tests such as hypothesis testing, skewness, z statistic, level of significance, and other necessary tests, as well as a discussion of the results obtained.
The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.
The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.
Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).
The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.
The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.
The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).
Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
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Si en total tiene 250 monedas que suman $42.50 ,Cuántas monedas de 25 centavos tiene en su alcancía?
Answer:
65 alojamiento
Step-by-step explanation:
HELPPPPPPPPPP
Which of the following is equivalent to the expression below ?
square root 8 minus square root 72 plus square root 50 ?
A. 13 square root 2
B. 7 square root 2
C. 3 square root 2
D. Square root 2
Answer:
a13 square root
..cv
..
..
the vertices of a triangle are P(-5,-7), Q(-3,-4), and R(2,-6)what are the vertices of the image reflected across the x axis
By definition, a Reflection is a transformation in which the figure is flipped over a line of reflection.
When a figure is reflected across the x-axis, the rule you must apply is the following:
\((x,y)\rightarrow\mleft(x,-y\mright)\)As you can notice, when a point is reflected across the x-axis, the sign of the y-coordinate changes.
In this case, you know that the vertices of the Pre-Image (the triangle PQR) are:
\(\begin{gathered} P\mleft(-5,-7\mright);Q\mleft(-3,-4\mright);R\mleft(2,-6\mright) \\ \end{gathered}\)Then, applying the rule, you get that the vertices of the Image (triangle P'Q'R'), are:
\(\begin{gathered} P\mleft(-5,-7\mright)\rightarrow P^{\prime}\mleft(-5,7\mright) \\ Q\mleft(-3,-4\mright)\rightarrow Q^{\prime}\begin{pmatrix}-3,4\end{pmatrix} \\ R\mleft(2,-6\mright)\rightarrow R^{\prime}\mleft(2,6\mright) \end{gathered}\)The answer is:
\(\begin{gathered} P^{\prime}(-5,7) \\ Q^{\prime}\begin{pmatrix}-3,4\end{pmatrix} \\ R^{\prime}(2,6) \end{gathered}\)Help pls I cant solve this problem
Answer:
12 x 9 x 15 is 1620. then start multiplication on the subject
what is the property of 3x(5x7)=(3x5)7
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
PLEASE HELP ASAP!! (Please do this if ur good at Scientific Notation) please tell me which 4 should I put in the box! (Click picture) ‼️‼️
Answer:
1st one is 6.9 X 10^6
2nd one is 2 x 10^5
Step-by-step explanation:
Mikas diner sold 70 milkshakes last week. 9% of the milkshakes had whipped cream on top. How many milkshakes with whipped cream were sold?
Step-by-step explanation:
I hope u got ur answer ;)
if u have any more doubt ask me
Answer:
7 milkshakes
Step-by-step explanation:
10% divide 70 = 1%
10 divede 70 is 7
1% is 7
9 times seven is 7 is 63
70-63 is 7
hope it helps
A 9 in the thousandths place has 10 times the value of a 9 in the ? Place.
Answer:
hundredths place
Answer:
ten thousandths place
Step-by-step explanation:
9 in the thousandths place is basically 0.009, and a 9 in the ten thousandths place is basically 0.0009, which multiplied by ten is 0.009