Answer: the mode is 67.2
Step-by-step explanation:
Given that;
Data Frequency
30 - 34 1
35 - 39 0
40 - 44 3
45 - 49 7
50 - 54 5
55 - 59 10
60 - 64 10
65 - 69 21
70 - 74 12
Mode = ?
we know that mode is the number that has the highest number of appearance of frequency, so in this case, the data group that has the highest frequency (21) is 65 - 69
Lower class boundary of the modal group; L = 65
Frequency of the group before the modal group; Fm-1 = 10
Frequency of the modal group; Fm = 21
Frequency of the group after the modal group; Fm+1 = 12
Group width; G = 4
Now using the formula
Mode = L + [ (Fm - Fm-1) / ( (Fm - Fm-1) + (Fm - Fm+1) ) ] × W
so we substitute
Mode = 65 + [ (21 - 10) / ( (21 - 10) + (21 - 12) ) ] × 4
= 65 + [ 11 / 20] × 4
= 65 + 2.2
= 67.2
Therefore the mode is 67.2
ABCDE is aregular pentangon
X=?
Answer:
x = 5.2
Step-by-step explanation:
Measure of interior angle of a regular polygon = [tex]\frac{(n-2)\times180}{n}[/tex]
Here n = number of sides of the polygon
Interior angle of a regular pentagon = [tex]\frac{(5-2)\times180}{5}[/tex]
= 108°
By applying cosine rule in ΔABK,
(BK)² = (AK)² + (AB)² - 2(AK)(AB)cos(108)°
(x + 3)² = 4² + 6² - 2(4)(6)cos(108)°
x² + 6x + 9 = 16 + 36 - (-14.83)
x² + 6x = 57.83
x² + 6x - 57.83 = 0
x = [tex]\frac{-6\pm \sqrt{6^2-4(1)(-57.83)}}{2(1)}[/tex]
x = [tex]\frac{-6\pm16.35}{2}[/tex]
x ≈ -11.2, 5.2
Since, x can't be negative,
x = 5.2 will be the answer.
Assume the random variable x is normally distributed with mean u=89 and standard deviation o=4. Find the indicated probability.
Answer:
4
Step-by-step explanation:
becouse is the rii asewei feel mw
I need help. (5+5)/2
Answer:5
Step-by-step explanation:10/2=5
Answer: the answer is 5
Step-by-step explanation
Write an equation that passes through the points (0,-5) and (8,-5)
Answer:
Equation of the line: [tex]y = -5[/tex].
Step-by-step explanation:
Let [tex](x_0,\, y_0)[/tex] and [tex](x_1,\, y_1)[/tex] denote the coordinates of these two points, respectively.
Calculate the slope [tex]m[/tex] of this line:
[tex]\displaystyle m = \frac{y_1 - y_0}{x_1 - x_0} = \frac{(-5) - (-5)}{8 - 0} = 0[/tex].
Notice that the slope is zero because the two points have the same [tex]y[/tex]-coordinates ([tex]y_0 = y_1 = -5[/tex]) even though their [tex]x[/tex]-coordinates are distinct ([tex]x_0 \ne x_1[/tex].)
Equation for this line in point-slope form:
[tex]y - y_0 = m\, (x - x_0)[/tex].
[tex]y - (-5) = 0\, (x - 0)[/tex].
Rewrite and simplify to obtain the equation of this line in slope-intercept form:
[tex]y = -5[/tex].
The [tex]x[/tex]-term was eliminated because the slope was zero.
A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). In this study, the explanatory variable is the
A. amount of eroded soil.
B. rate of water flow.
C. depth of the soil bed.
D. size of the soil bed.
E. None of the above.
Answer:
B. rate of water flow.
Step-by-step explanation:
Given that in a research study the explanatory variable is a form of a variable that is independent and it is used by the researcher to make predictions or analyze variations in other variables known as response variables.
Hence, in this case, the Explanatory variable is the "rate of water flow" because it is the variable researcher wishes to utilize in predicting the amount of soil washed away.
The temperature in Tampa increased from 4 a.m. to 4 p.m. on one day in February the tables of values below represents temperatures as a function of time
Answer:
from 6:53 a.m. to 8:53 a.m.
Step-by-step explanation:
:)
Maria and Jane set up a lemonade stand one summer to earn money for a trip to the beach. They noticed that the hotter the day, the more glasses of lemonade they sold. They mixed up the lemonade exactly the same way every day: the same amount of sugar, lemon juice, and water. They added ice to the glass when they poured the drink. They always used the same size glass. They decided to chart their sales in order to figure out how much lemonade to make each day, using the weather forecast as their guide. Identify the independent, dependent, and controlled variables in the girls' experimental data.
Answer:
When its hotter people loose water by sweating (de-hydrating) and they replenish their bodies with Lemonade. PLEASE MARK ME BRAINLIEST!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 9 cm
Answer:
8 cm and 9 cm
Step-by-step explanation:
This is the answer because:
1) The other two sides have to equal somethinng that is bigger than 13.
2) 5 cm + 8 cm = 13 cm, therefore, 5 cm and 8 cm is not the correct answer.
3) 6 cm + 7 cm = 13 cm, therefore, 6 cm and 7 cm is not the correct answer.
4) 7 cm + 2 cm = 9 cm, therefore, 7 cm and 2 cm is not the correct answer.
5) Finally, 8 cm + 9 cm = 17 cm, therefore, it is the correct answer since it has a bigger value than 13.
Hope this helps! :D
Answer:
8 and 9
Step-by-step explanation:
because
What is 4/5 as a decimal and what is 4/5 as a percent representation
Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a
congruence statement,
If no, justify your answer.
Step-by-step explanation:
Angle ACB = Angle ZXY (given)
AB = XY (given)
CB = ZY (given)
Since they both display the SSA postulate, it does not guarantee that the triangles are congruent.
Answer:
NoStep-by-step explanation:
Given
Two sides and non-included angle of one triangle is congruent to same on another triangleIt doesn't match any congruency postulates and therefore is not enough to proof that the triangles are congruent
What is the awnser please!! -5r + 6 < -5(r + 2)
Find the amount of simple interest that $400 would earn at 8% per year by the end of 3 1/2 years.
Answer:
$32
Step-by-step explanation:
A pizza chef begins to spin a constant volume of dough to make a pie by spinning and tossing the dough into the air, such that the dough takes on a cylindrical shape. The dough's radius increases while the height decreases, but the dough remains a cylinder. At time t = tı, the height of the dough is 1/2 inch, the radius of the dough is 16 inches, and the radius of the dough is increasing at a rate of 2 inches per minute.
Required:
a. At time tı, at what rate is the area of the "top" of the pizza (the part with the toppings) increasing with respect to time? Show the computations that lead to your answer, and indicate units of measure.
b. At time tı, at what rate is the height of the dough decreasing with respect to time?
Answer:
a ) dAt/dt = 50,24 in/min
dh/dt = - 0,125 in/min
Step-by-step explanation:
The area of the top is At :
At = π*r²
a) Tacking derivatives with respect to time:
dAt/dt = 2* π*r * dr/dt
At t = t₁ r = 16 in and dr/dt = 0,5
Then
dAt/dt = 2*3,14*16*0,5 in/min
a ) dAt/dt = 50,24 in/min
b) The volume of the cylinder is:
Vc = π*r²*h ( where h is the heigh of the cylinder )
Tacking derivatives with respect to time
dVc/dt = 2* π*r*h*dr/dt + π*r²*dh/dt
But dVc/dt = 0 since the volume remains constant, then:
π*r²*dh/dt = - 2* π*r*h*dr/dt
r*dh/dt = - 2*h*dr/dt
dh/dt = - 2*0,5*2/16 in/min
dh/dt = - 0,125 in/min
i)1-2(2x+1)=1-(x-1)
ii)3.6x-6.1=5.9_2.4x
question from equation and inequality
Answer:
1)Solving the expression [tex]1-2(2x+1)=1-(x-1)[/tex] we get [tex]\mathbf{x=-\frac{1}{3}}[/tex]
2) solving the equation [tex]3.6x-6.1=5.9-2.4x[/tex] we get [tex]\mathbf{x=2}[/tex]
Step-by-step explanation:
We need to solve the expressions:
1) [tex]1-2(2x+1)=1-(x-1)\\[/tex]
Solving
[tex]1-2(2x+1)=1-(x-1)[/tex]
First solving the brackets
[tex]1-4x-2=1-x+1[/tex]
Simplifying
[tex]-1-4x=-x[/tex]
Adding 4x on both sides
[tex]-1-4x+4x=-x+4x\\-1=3x[/tex]
Switching the sides
[tex]3x=-1[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=-\frac{1}{3}\\x= -\frac{1}{3}[/tex]
So, Solving the expression [tex]1-2(2x+1)=1-(x-1)[/tex] we get [tex]\mathbf{x=-\frac{1}{3}}[/tex]
2) [tex]3.6x-6.1=5.9-2.4x[/tex]
Solving:
[tex]3.6x-6.1=5.9-2.4x[/tex]
Adding 6.1 on both sides
[tex]3.6x-6.1+6.1=5.9-2.4x+6.1\\3.6x=12-2.4x[/tex]
Adding 2.4x on both sides
[tex]3.6x+2.4x=12-2.4x+2.4x\\6x=12\\[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{12}{6}\\x=2[/tex]
So, solving the equation [tex]3.6x-6.1=5.9-2.4x[/tex] we get [tex]\mathbf{x=2}[/tex]
Simplify to create an equivalent expression6(7-3y)+6(y+1)
Answer:
48-12y
Step-by-step explanation:
6(7-3y) + 6(y+1)
distribute the 6 on both parentheses
42-18y+6y+6
combine like terms
42-12y+6
combine like terms again
48-12y
Determine the x-intercept of the line whose equation is given: Y = 4x + 2
a. (0, 2)
b. (-2, 0)
c. (0, - 1/2
d. (- 1/2, 0)
Answer:
d
Step-by-step explanation:
Find the distance between the points (-12.3, 15.1) and (17.5, 2). Round your answer to the
nearest hundredth.
Answer:
32.55
Step-by-step explanation:
d = 32.552266
For:
(X1, Y1) = (-12.3, 15.1)
(X2, Y2) = (17.5, 2)
Distance Equation Solution:
d=(17.5−(−12.3))2+(2−15.1)2−−−−−−−−−−−−−−−−−−−−−−−−−√
d=(29.8)2+(−13.1)2−−−−−−−−−−−−−−−√
d=888.04+171.61−−−−−−−−−−−−−√
d=1–√059.65
d=32.552266
could be confusing.
Identify whether each phrase is an expression, equation, or inequality
Answer:
Top stays the same
Middle and bottom switch
Step-by-step explanation:
Of the following sets, which represents a function?
Situation A = {student's name, all the colors that the student likes}
Situation B = {student's name, the student's favorite math teacher}
a. Only A
b. Only B
c. Both A and B
d. Neither A nor B
Answer:
Situation B is a function.
Step-by-step explanation:
We know that,
A function is a relation in which every element in the domain i mapped to a unique element in the co-domain.
That is, every element in the domain must have a unique image.
So, we see that,
Situation A = {student's name, all the colors that the student likes}
Here, the students can have more than one color which they like.
Thus, this relation is not a function.
Situation B = {student's name, the student's favorite math teacher}
Here, the students can have only one favorite math teacher.
So, this relation is a function.
Answer:
D
Step-by-step explanation:
Divide. Give the Divide. Give the quotient and remainder.
254 divided 8
Quotient:
Remainder:
Step-by-step explanation:
254 = 8 * 30 + 8 * 1 + 6
= 8(30 + 1) + 6
= 8 * 31 + 6.
Hence the quotient is 31 and the remainder is 6.
Answer:
254/8=31.75
Step-by-step explanation:
The remainder of 254 divided by 8 is 6
Solve the inequality for y.
y-5<-14
Approximately 24% of the calls to an airline reservation phone line result in a reservation being made. (a) Suppose that an operator handles 15 calls. What is the probability that none of the 15 calls result in a reservation
g According to government data, 25% of employed women have never been married. If 10 employed women are selected at random, what is the probability that two or fewer of them have never been married
Answer:
The probability is 0.5263
Step-by-step explanation:
Probability of employed women being unmarried = 25% = 0.25 ( let this be p)
Probability of employed women ever being married = 1-0.25 = 0.75 (let this be q)
Now, we want to calculate the probability that two or less have never been married
We can use the Bernoulli approximation of the Binomial distribution here;
In this case, we have three cases
We have cases of;
Exactly two + Exactly one + None
For exactly two;
10 C 2 0.25^2 0.75^8 = 0.282
For exactly one
10 C 1 0.25^1 0.75^9 = 0.188
For none
10C 0 0.25^0 0.75^10 = 0.0563
Adding these 3 to get the probability of two or fewer, we have;
0.0563 + 0.188 + 0.282 = 0.5263
Two cars start from the same point and move in a straight line, one east at a speed of 60 km per hour and the other west at a speed of 80 km per hour. After what time will they live at a distance of 770 km?
Answer:
5.5 hours
Step-by-step explanation:
Given that :
Speed of A = 60 kmphr
Speed of B = 80 kmphr
After what time will distance = 770 km
Speed * Time = Distance
Let time = x
Distance A + Distance B = 770
(60 * x) + (80 * x) = 770
60x + 80x = 770
140x = 770
x = 770 / 140
x = 5.5 hours
Grant paid $12 for 4 baseball card packs. How many baseball card packs can he purchase for $21? Group of answer choices
Answer:
Grant can purchase 7 baseball card packs for $21. 12/4=3 and 21/3=7.
Answer: 7
Step-by-step explanation:
Answer:
7 packs
Step-by-step explanation:
12/4 = $3 ea.
21/3 = 7 packs
An ostrich that is it so many inches tall is 12 in taller than three times the height of a kiwi. What is the height of a kiwi in inches?
Answer:
the height should be 4.
Step-by-step explanation:
because 12 divided by 3 is 4
Maya's penny bank is 3/4 full. After she removes 280 pennies, it is 1/2 full. How many pennies can Maya's bank hold?
Answer:
1120
Step-by-step explanation:
write a function for the table
please help I don't get it
Answer:
y=2(x-2.5)
Step-by-step explanation:
Answer:
y = 2x - 5
Step-by-step explanation:
Let us consider the points (- 2, - 9) & (0, - 5)
Equation of line in two point form is given as:
[y-(-9)]/[-9-(-5)] = [x - (-2)]/[-2 - 0]
(y + 9)/(-9 +5) = (x + 2)/ (-2)
(y + 9)/(-4) = (x + 2)/(-2)
(y + 9)/(2) = (x + 2)/(1)
(y + 9) = 2(x + 2)
y + 9 = 2x + 4
y = 2x + 4 - 9
y = 2x - 5
This is the required function.
Given ΔMNO, find the measure of ∠MNO.
Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent.
28 degrees
38 degrees
52 degrees
76 degrees
I know the answer is 28 degrees , I just am not sure how to work out this problem .
Answer:10907
Step-by-step explanation 10907
Answer:
The answer is 28
Step-by-step explanation:
Hope this helps,
have a great day
Alan jogged 3.2 miles to school and then 2.2 after school each day for 5 days. Jennifer jogged a total of 45 miles. Who jogged the most and by how much?
Answer:
Jennifer jogged the most, by 18 miles
Step-by-step explanation:
Given
Alan:
[tex]To\ School = 3.2\ miles[/tex]
[tex]After\ School = 2.2\ miles[/tex]
[tex]Days = 5[/tex]
Jennifer:
[tex]Total= 45\ miles[/tex]
Required
Who jogged most?
First, we calculate the distance covered by Alan daily
[tex]Daily = To\ School + After\ School[/tex]
[tex]Daily = 3.2\ miles + 2.2\ miles[/tex]
[tex]Daily = 5.4\ miles[/tex]
Next, we calculate the distance covered in 5 days
[tex]Distance = 5.4\ miles * 5[/tex]
[tex]Distance = 27\ miles[/tex]
By comparison, Jennifer jogged the most because 45 > 27
And the difference is:
[tex]Difference = 45\ miles - 27\ miles[/tex]
[tex]Difference = 18\ miles.[/tex]