A coin is flipped, and a number cube is rolled. What is the probability of getting heads on the coin and a number less than 3 on the number cube?
a.one eighth
b. one sixth
c. one fourth
d. one half
Answers
=============================================================
Explanation:
The probability of getting heads is 1/2 because there's one side we want out of two sides total
The probability of getting less than 3 is 2/6 = 1/3 since we have two sides we want (rolling a "1" or a "2") out of six sides total.
Multiply the two mentioned fractions: 1/2 times 1/3 = 1/6
1/6 can be written as "one sixth", but I prefer the first format better since it's shorter.
---------------
If you are a visual learner, you can make a table with 2 rows and 6 columns, or vice versa (6 rows and 2 columns). The order doesn't matter.
The two rows represent the events Heads or Tails. The 6 columns show the different outcomes on the number cube. We have 6*2 = 12 different outcomes of rolling a die and flipping a coin.
Of those 12 outcomes, shade in 2 boxes to represent getting heads and either a "1" or "2". Refer to the diagram below.
We have 2 shaded rectangles out of 12 total to get 2/12 = 1/6
The visual representation of a table like this may help show why we multiplied the fractions 1/2 and 1/3 to get the answer. Hint: think of area = length*width.
The probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
A coin is flipped, and a number cube is rolled.
We need to find the probability of getting heads on the coin and a number less than 3 on the number cube.
The probability of getting heads when flipping a coin is 1/2
The probability of getting less than 3 is 2/6 = 1/3 since we have two sides
Now the probability of getting heads on the coin and a number less than 3 on the number cube
The product of 1/2 and 1/3
1/2×1/3
1/6
Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is 1/6, Option A is correct.
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ2
Related Questions
Tami earned $20.64 in simple interest by investing a principal of $400 in a Treasury bill.
If the interest rate was 1.72%/a, for how many years did she have her investment?
Answers
The number of years she had her investment is after 3 years
How to determine the years of investment?From the question, the given parameters are:
Principal Amount, P = $400Interest Rate, r = 1.72%Simple Interest, I = $20.64The number of years (T) is calculated from the following simple interest formula
I = PRT
Substitute the given parameters in the above equation
20.64 = 400 * 1.72% * t
Express 1.72% as decimal without percentage
20.64 = 400 * 0.0172 * t
Evaluate the product
20.64 = 6.88 * t
Divide both sides by 6.88
20.64/6.88 = 6.88/6.88 * t
Evaluate the quotient
3 = t
Rewrite the equation as
t = 3
This means that she had her investment after 3 years
Hence, the number of years she had her investment is after 3 years
Read more about simple interest at:
https://brainly.com/question/25845758
#SPJ1
Distribute to create an equivalent expression with the fewest symbols possible.
7(4p + 2q + 3r) =7(4p+2q+3r)
Answers
The equivalent expression for the given expression is 28p + 14q + 21r.
What is an equivalent expression?An expression that gives the same value as the original expression when the same value of a variable is substituted is said to be an equivalent expression.
An equivalent expression is simplified to the original expression by using the distributive property.
What is distributive property?The distributive property is
a(b + c) = ab + ac
Calculation:The given expression is 7(4p + 2q + 3r)
Applying the distributive property,
7(4p + 2q + 3r) = 7(4p) + 7(2q) + 7(3r)
⇒ 28p + 14q + 21r
Thus, the equivalent expression for the given expression is 28p + 14q + 21r.
Learn more about an equivalent expression here:
https://brainly.com/question/11352551
#SPJ1
7(4p+2q+3r)=7(4p+2q+3r)
Apply distributive law
a(b+c)=ab+acSo
28p+14q+21r=28p+14q+21rThis is the required expression
A textbook store sold a combined total of 204 math and psychology textbooks in a week. The number of math textbooks sold was three times the number of psychology textbooks sold. How many textbooks of each type were sold?
Answers
153 math textbooks
Let’s let x equal the number of psychology textbooks sold. That means that the number of math textbooks sold would be 3x (3 times x, or the number of psychology textbooks). Knowing the total is 204, we can make an equation that says x (the number of psychology textbooks) plus 3x (the number of math textbooks) equals 204 (the total number of textbooks). We can then combine x plus 3x to make 4x. So we’re left with 4x equals 204. If we divide both sides of the equation by 4 we’re left with x equals 51. So 51 psychology textbooks were sold. We then multiply this number by three to get 153, the number of math textbooks sold.
Let x = number of psychology textbooks
So 3x = number of math textbooks
x + 3x = 204
4x = 204
x = 51 3x = 3(51) = 153
A total of 204 textbooks were sold with 153 math textbooks and 51 psychology textbooks being sold, as the number of math textbooks was three times the number of psychology textbooks.
Given that,
The combined total of math and psychology textbooks sold in a week is 204.
The number of math textbooks sold is three times the number of psychology textbooks sold.
To solve this problem,
Assign variables to represent the number of math and psychology textbooks sold.
Let's say "M" represents the number of math textbooks and "P" represents the number of psychology textbooks.
We know that the combined total of math and psychology textbooks sold is 204,
So the equation be:
M + P = 204 .....(i)
We are also given that the number of math textbooks sold was three times the number of psychology textbooks sold.
In equation form, this can be expressed as:
M = 3P
Now, we can substitute the value of M in terms of P into the equation (i):
3P + P = 204
Combining like terms, we get:
4P = 204
Dividing both sides by 4, we find:
P = 51
So, the number of psychology textbooks sold is 51.
To find the number of math textbooks sold,
Substitute this value back into the equation:
M = 3P
M = 3(51)
M = 153
Therefore, the number of math textbooks sold is 153.
Hence,
153 math textbooks and 51 psychology textbooks were sold.
To learn more about word problem visit:
https://brainly.com/question/29203255
#SPJ4
The mean of a normally distributed data set is 110, and the standard deviation is 15.
a) Use the standard normal table to find the probability that a randomly-selected data value is greater than 95.
b) Use the standard normal table to find the probability that a randomly-selected data value is greater than 125.
Answers
From the standard normal table, the respective probabilities are; 0.908 and 0.841
How to find the probability from z-score?
Formula for calculating the standard score or z score is:
z = (x - μ)/σ
where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
A) We are given;
x = 95
μ = 110
σ = 15
Thus;
z = (95 - 110)/15
z = 1.33
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.091759.
P(x > 95) = 0.908
B) We are given;
x = 125
μ = 110
σ = 15
Thus;
z = (125 - 110)/15
z = 1
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.158655.
P(x > 95) = 0.841
Read more about Probability from z-score at; https://brainly.com/question/25638875
#SPJ1
In the circle below, O is the center and mGl= 145°. What is the measure of the central angle ZGOR? H G 0 145° I
Answers
The measure of the central angle is 290 degrees
How to determine the measure of the central angle?The measure of arc GI is given as:
mGI = 145 degrees
The measure of the central angle is calculated as:
Central angle = 2 * mGI
Substitute the known values in the above equation
Central angle = 2 * 145
Evaluate the product
Central angle = 290
Hence, the measure of the central angle is 290 degrees
Read more about central angles at:
https://brainly.com/question/16736105
#SPJ1
Write the following number in scientific notation.
788,000
Answers
Because 788 x 1000 = 788000
Answer:
788,000 =
788 x 10^3
78.8 x 10^4
7.88 x 10^5
.788 x 10^6
and so on
(02.03)
Figure ABCD is transformed to A′B′C′D′, as shown:
A coordinate plane is shown. Figure ABCD has vertices A at 3 comma 1, B at 3 comma 4, C at 5 comma 5 and D at 5 comma 3. Figure A prime B prime C prime D prime has vertices A prime at negative 5 comma 1, B prime at negative 5 comma 4, C prime at negative 7 comma 5 and D prime at negative 7 comma 3.
Which of the following sequences of transformations is used to obtain figure A′B′C′D′ from ABCD? (4 points)
Group of answer choices
Reflection about the x-axis followed by a translation right by 2 units
Reflection about the y-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
Answers
The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units
What is the type of Transformation used?
As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.
Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).
Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)
Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).
Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).
This is the coordinates for A'.
Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.
Read more about Transformation Types at; https://brainly.com/question/4289712
#SPJ1
Inverse Functions: Mastery Test
Select the correct answer.
Consider this function.
f(x) = -3z + 3
Which graph represents the inverse of function f
Answers
The inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]x=g(y)=-\frac{y}{3}+1[/tex].
How to find the inverse of a function of type y=f(x)=ax+b?An inverse function is a function that undoes the action of another function. For example, if the function [tex]f[/tex] produces the number [tex]y[/tex] after applying on [tex]x[/tex] i.e., [tex]y=f(x)[/tex], then the inverse function of [tex]f[/tex], which is denoted by [tex]f^{-1}[/tex], produces [tex]x[/tex] after applying on [tex]y[/tex] i.e., [tex]f^{-1}(y)=x[/tex].To find the inverse of a function of type [tex]y=f(x)=ax+b[/tex], we just need to rewrite the equation as [tex]x=g(y)[/tex] which can be illustrated as follows: [tex]y=ax+b\Longrightarrow x=\frac{y}{a}-\frac{b}{a}[/tex] i.e., [tex]g(x)=\frac{x}{a}-\frac{b}{a}[/tex] is the inverse function of [tex]f(x)=ax+b[/tex].Here, the given function is [tex]f(x)=-3x+3[/tex].
Then we get:
[tex]y=-3x+3\\\Longrightarrow x=-\frac{y}{3}+1[/tex]
Thus, the inverse function of the function [tex]f(x)=-3x+3[/tex] will be [tex]g(x)=-\frac{x}{3}+1[/tex].
The graph representing this inverse function is given as follows:
To know more about inverse function, refer: https://brainly.com/question/3831584
#SPJ9
What is the converse of the conditional statement?
If x is even, then x + 1 is odd.
O If x is not even, then x + 1 is not odd.
O If x + 1 is odd, then x is even.
If x + 1 is not odd, then x is not even.
OIf x is even, then x + 1 is not odd.
Mark this and return
Save and Exit
Next
Submit
Answers
The correct answer is If x + 1 is odd, then x is even.
What is the converse of the conditional?A conditional statement's opposite is produced when the hypothesis and conclusion are switched around. The conditional statement is known as p q in geometry. q p is how people refer to the Converse.One can obtain the contrary assertion by switching "p" and "q locations "in the condition. An example of a condition is "If Cliff is thirsty, then she drinks water." If Cliff drinks water, then she is thirsty, is the converse of the first sentence.The four primary varieties of conditional phrases are Zero Conditional, First Conditional, Second Conditional, and Third Conditional.The converses of the conditional statement:
"If q then p" provides the converse statement to the conditional expression "If p then q."
The converse of the conditional statement is If x + 1 is odd, then x is even.
To learn more about the conditional statements, refer to:
https://brainly.com/question/12830978
#SPJ9
Look for a pattern in the data set to determine which kind of model best describes the data.
Running Speed of a Human
Distance Traveled
(miles)
1
2
3
4
Average Speed
(miles per hour)
7
6.3
5.67
5.103
The data appear to be linear.
The data appear to be quadratic.
The data appear to be cubic.
The data appear to be exponential.
Answers
On looking for a pattern in the given data set, the quadratic model best describes the data.
2nd option is correct.
A data model represents the type of relationship between the variables of a data set.
Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.
Given data is:
Distance Traveled Average Speed(miles per hour)
(miles)
1 7
2 6.3
3 5.67
4 5.103
A quadratic model is the best data model for the given data set.
The pattern observed in the given data set observes the properties of a quadratic function.
Learn more about data models here:
https://brainly.com/question/28059450
#SPJ1
Answer:
Exponential is the correct answer.
Step-by-step explanation:
50 POINTS! Plot function h on the graph.
NO LINKS
Answers
See attachment for the graph of the piecewise function h(x)
How to plot the function?The function is given as:
h(x) = | -4, x < 3
| x + 5, x >= 3
The above function is a piecewise function.
It has 2 separate functions at two domains
This means that we plot the sub-functions in the piecewise function at their respective domain
See attachment for the graph of the piecewise function h(x)
Read more about piecewise function at:
https://brainly.com/question/27262465
#SPJ1
4 1/3 - 1 2/3 how to solve this please
Answers
Answer:
[tex]2\frac{2}{3}[/tex]
Step-by-step explanation:
1) Convert [tex]4\frac{1}{3}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].
[tex]\frac{4\times3+1}{3} -1\frac{2}{3}[/tex]
2) Simplify 4 * 3 to 12.
[tex]\frac{12+1}{3}[/tex]
3) Simplify 12 + 1 to 13.
[tex]\frac{13}{3} -1\frac{2}{3}[/tex]
4) Convert [tex]1\frac{2}{3}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].
[tex]\frac{13}{3} -\frac{1\times3+2}{3}[/tex]
5) Simplify 1 * 3 to 3.
[tex]\frac{13}{3} -\frac{3+2}{3}[/tex]
6) Simplify 3 + 2 to 5.
[tex]\frac{13}{3} -\frac{5}{3}[/tex]
7) Join the denominators.
[tex]\frac{13-5}{3}[/tex]
8) Simplify.
[tex]\frac{8}{3}[/tex]
9) Convert to mixed fraction.
[tex]2\frac{2}{3}[/tex]
(Decimal Form: 2.666667)
Thank you,
Eddie
Two sides of a triangle are 5 and 55 cm. Complete the inequality to show the possible lengths of the third side. If the third side of the triangle is x then...
Answers
The third side of the triangle falls between (50, 60).
How to find the third side of a triangle?Inequality triangle theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, the other two sides are 5 cm and 55 cm. The range of the third side x can be computed using inequality triangle theorem.
Hence,
x < 5 + 55
x < 60
And,
x > 55 - 5
x > 50
Therefore, 50 < x < 60.
Hence, the third side of the triangle falls between (50, 60).
learn more on triangle here: https://brainly.com/question/1163433
#SPJ1
. Which of the following statements is not true?
a. If x = 1, then x² = 1.
b. If x²= 1, then x = 1.
c. If x=-1, then x² = 1.
d. x² = 1.if and only if x = 1 or x = -1.
Answers
Answer:
If x^2 = 1, then x = 1 is NOT true because x can also be -1.
Find the value of x.
answer choices
A. 70
B. 65
C. 30
D. 40
Answers
The value of x is 70°. The correct option is A. 70
Circle GeometryFrom the question, we are to determine the value of the measure of arc x
From one of the circle theorems, we have that
The angle subtended by an arc at the center is twice the angle subtended by it at any point on the circumference.
First, we will determine the value of the third angle in the triangle formed.
Let the angle be y
y + 15° + 20° = 180°
∴ y = 180° - 15° - 20°
y = 145°
Now, the angle supplementary to this is the angle the arc subtends at the circumference.
Thus,
The angle at the circumference = 180° - 145°
The angle at the circumference = 35°
From the above theorem, we can conclude that the angle subtended by the arc at the center of the circle is 2 × 35° = 70°
∴ The measure of the arc is 70°
This is the value of x
Hence, the value of x is 70°. The correct option is A. 70
Learn more on Circle Geometry here: https://brainly.com/question/19529058
#SPJ1
Consider the following figure:
Answers
Answer:
angle <B = 76
Step-by-step explanation:
The measure of an exterior angle is equal to sum of two interior angles that is not adjacent to the exterior angle.
We can write the following equation with this information to find the value of angle <B
<B + 71 = 147 subtract 71 from both sides
<B = 76
A bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km away. Write a formula expressing the dependence of the variable s on t, where s is the distance between the bicyclist and the station in km, t - the duration (time) of his travel in hours. Using the formula, find: d for t=3.5
Answers
1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t
2. the distance travelled at time t = 3.5 h is 18 Km
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
1. How to determine the formula expressing the dependence of the variable s on tFrom the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.
Thus, we shall determine the distance travel in time t as follow
Speed = 12 Km/hTime = tDistance in time t = ?Speed = distance / time
12 = distance / t
Cross multiply
Distance = 12 × t
Distance in time t = 12t
But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:
s = 60 - 12t
Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t
2. How to determine the distance at t = 3.5 hoursThe distance at t = 3.5 hours can be obtained as illustrated below:
Time (t) = 3.5 hoursDistance (s) = ?s = 60 - 12t
s = 60 - (12 × 3.5)
s = 60 - 42
s = 18 Km
Thus, the distance travelled at t = 3.5 hours is 18 km
Learn more about speed:
https://brainly.com/question/680492
#SPJ1
The legs of a right triangle measure 3 cm and 8 cm. What is the length of the hypotenuse?
Answers
PLEASE HELP ME WITH THIS PROBLEM!!!
Answers
Answer: Moderate negative association
Step-by-step explanation:
a negative association or in other terms correlation, suggests that while one variable increases the other decreases and vice versawhen looking at the graph, the data shows a negative correlationas the x variable increases the y variable decreasesthis not a perfect correlation as the the change in value of variable x is not directly proportional to the change in value of yThe bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed.
Estimate the percent of apartments residents who pay less than $650 per month.
A. 99%
B. 25%
C. 68%
D. 30%
Answers
Answer: 30%
Step-by-step explanation:
the first 2 bars < or = to 650 add up to ~29% roughly, cant be 25%, 68%, or 99%. Therefore the only answer available is 30%
Answer:
30%
Step-by-step explanation:
For Connexus students its 30% :)
need heeeelp please
Answers
Answer:
please how
Step-by-step explanation:
I will help ypu
Can anyone please help me with this assignment
Answers
1. The sentences translated to equations looks like:
a) 4x = 32.
b) x + 6y = 43.
c) 3x + 7 = 9x - 4.
d) 76 - 2x = 8x.
2. The equations translated to sentences looks like:
a) The sum of 16 and 9 times x is 50.
b) The sum of the square of x and 6 times y is 4 times w.
c) Three times x is 52.
d) Five-sixth is equal to the product of -10 and x.
Practice Part 1: Translate sentence to equation
a)Four times a number is thirty-two.
Assuming the number to be x, we get the equation, 4x = 32.
b)The sum of and six times is equal to forty-three.
The sentence, when translated to an equation looks like, x + 6y = 43.
c)The sum of 7 and three times equals the difference of 9 times and 4.
The sentence, when translated to an equation looks like, 3x + 7 = 9x - 4.
d)Two times less than 76 is equal to the product of 8 and
The sentence, when translated to an equation looks like, 76 - 2x = 8x.
Practice Part 2: Translate equation into sentence
a) 9x + 16 = 50.
- The sentence for the given equation is, the sum of 16 and 9 times x is 50.
b) x² + 6y = 4w.
- The sentence for the given equation is, the sum of the square of x and 6 times y is 4 times w.
c) 3x = 52.
- The sentence for the given equation is, three times x is 52.
d) 5/6 = -10x.
- The sentence for the given equation is, five-sixth is equal to the product of -10 and x.
Learn more about translating sentences and equations at
https://brainly.com/question/13155862
#SPJ1
In a village the cases of a particular infectious disease have been exponentially decreasing at a rate of 95% per year since the pople started receving the vaccine. If there were 200 cases in the village to start with, predict the number of cases after 2 years. First complete the equation:
Remaining amount=
Answers
The number of cases after two years is 221.
What is the number of cases after two years?As a result of the disease, the population of the village would decrease by 95% per year. The number of cases at the village is function of the rate of infection, the number of years and the beginning number of cases.
The exponential function that can be used to represent this situation is:
FV = P( 1 + r)^t
FV = Future value P =beginning number of casesR = rate of increase in the number of cases : 100% - 95% = 5%t = timeFV = 200 (1.05)^2 = 221
To learn more about exponential functions, please check: https://brainly.com/question/26331578
#SPJ1
There is a set of 12 cards numbered 1 to 12. A card is chosen at random. Event A is choosing a number less
than 6. Event B is choosing a number divisible by 3. A diagram is given below.
(Can you help with #4 if you know it:)
Answers
The number of permutations of picking 4 pens from the box is 30.
There are six different unique colored pens in a box.
We have to select four pens from the different unique colored pens.
We have to find in how many different orders the four pens can be selected.
What is a permutation?A permutation is the number of different arrangements of a set of items in a particular definite order.
The formula used for permutation of n items for r selection is:
[tex]^nP_r = \frac{n!}{r!}[/tex]
Where n! = n(n-1)(n-2)(n-3)..........1 and r! = r(r-1)(r-2)(r-3)........1
We have,
Number of colored pens = 6
n = 6.
Number of pens to be selected = 4
r = 4
Applying the permutation formula.
We get,
= [tex]^6P_4[/tex]
= 6! / 4!
=(6x5x4x3x2x1 ) / ( 4x3x2x1)
= 6x5
=30
Thus the number of permutations of picking 4 pens from a total of 6 unique colored pens in the box is 30.
Learn more about permutation here:
https://brainly.com/question/14767366
#SPJ1
How many three-digit positive integers have three different digits and at least one prime digit?
Answers
Answer:
252
Step-by-step explanation:
using a brute force method in c++
#include <stdio.h>
int main(){
int a, b, c, n = 0;
for(a = 1; a <= 9; a++)
for(b = 0; b <= 9; b++)
for(c = 0; c <= 9; c++)
if((a==3 || b==3 || c==3)) n++;
printf("%d\n", n);
}
Let x, y, z be three natural numbers such that x < y < z. If GCF(x, y, z) = 3, GCF (y, z) = 15, LCM (x, y, z) = 3150, and x is even number greater than 10, then find the values of x, y and z.
Answers
Answer:
one of several possible solutions :
18, 75, 105
Step-by-step explanation:
prime factors of 3150 :
3150 ÷ 2 = 1575
1575 ÷ 2 no
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 3 no
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 5 no
7 ÷ 7 = 1
3150 = 2¹ × 3² × 5² × 7¹
these are the product of the longest streaks of prime factors in x, y and z.
the GCF(y, z) = 15.
the prime factors of 15 are simply 3¹×5¹.
so, y and z share only the factors 3 and 5.
the GCF(x, y, z) = 3.
since x is an even number, the elimination of 5 in the GCF is not surprising.
let's try the following :
x = 2¹ × 3² = 2×9 = 18
y = 3¹ × 5² = 3×25 = 75
z = 3¹ × 5¹ × 7¹ = 3×5×7 = 105
that uses all the factors of 3150, and their LCM is as the product of the longest streaks of their prime factors is
2¹ × 3² × 5² × 7¹.
fits.
the GCF(75, 105) is the product of the prime factors they have in common : 3¹ × 5¹ = 15.
fits.
the GCF(18, 75, 105) is the product of the prime factors ask 3 numbers have in common, which is only 3¹ = 3.
fits.
18 < 75 < 105
fits.
18 is an even number greater than 10.
fits.
there are more than 1 solutions.
e.g.
z = 2¹ × 3¹ × 5¹ × 7¹ = 210
is also possible.
Alicia wanted to lose some weight, so she planned a day of exercising. She spent a total of 3 hours riding her bike and jogging. She biked for 12 miles and jogged for 12 miles. Her rate for jogging was 6 mph less than her biking rate. What was her rate when jogging?
Please answer asap thank you :)
Answers
Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:
[tex]v = \frac{12}{t}[/tex]
Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:
[tex]v + 6 = \frac{12}{3 - t}[/tex]
[tex]v = \frac{12}{3 - t} - 6[/tex]
Then:
[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]
[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]
[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]
18t - 6t² = 24t - 36
6t² + 6t - 36 = 0
t² + t - 6 = 0
(t + 3)(t - 2) = 0. -> t = 2 hours.
Hence her jogging rate in mph is given as follows:
[tex]v = \frac{12}{2} = 6[/tex]
More can be learned about the relation between velocity, distance and time at brainly.com/question/24316569
#SPJ1
Half a foot by a quarter of a foot by 3/4 of a foot fraction
Answers
Step-by-step explanation:
x×1/2×1/4×3/4
x×3/32
3/32x
Which of the following is a whole number that can be divided into another given
number without leaving a remainder?
Term
Multiple
Factor
Variable
Answers
Answer:
(c) Factor
Step-by-step explanation:
The constituents of a product are its factors.
Dividing a product by one of its factors will not leave a remainder.
__
A term is a constant or product of one or more variables and a constant. For example, -4 and 24xy are both terms.
A multiple is a product with one factor being an integer. For example, 3×1.5 = 4.5 is a multiple of 1.5.
A variable is a symbol for an unknown value. Commonly, a variable is a single letter, but may also be a blank (__) or a question mark (?). Sometimes a word or phrase is used as a variable. For example, ...
3 + x = 5
3 + __ = 5
3 + ? = 5
3 + (some number) = 5
Please help me w this question! ASAPP
Answers
Answer: None of these are correct
Step-by-step explanation:
I believe that the equation is showing transitive property.
