Final answer:
To calculate the probability that Bob will draw $15 in tokens, we need to calculate the probability of him drawing a $5 token from the cup (1/3) and a $10 token from his pocket (2/3) and then multiply these probabilities to get the total probability (2/9).
Explanation:
The probability that Bob will draw $15 in tokens consists of two steps: drawing from the coin cup and then drawing from his pocket. We must calculate the probability for each stage and, finally, multiply these probabilities together to get the total probability of drawing $15.
From the cup, Bob can draw either a $1 token or a $5 token. To get a total of $15, Bob would need to draw a $5 token from the cup, since the highest value in his pocket is $25 and 1+25 is greater than 15. There are two $5 tokens in the cup among six tokens in total, so the probability of drawing a $5 token is 2/6 or 1/3.
Having drawn a $5 token, he now needs to draw a $10 token from his pocket to reach the total of $15. In his pocket, he has two $10 tokens and one $25 token, making three tokens in total. The probability of drawing a $10 token is therefore 2/3.
By multiplying these probabilities, we get the total probability of drawing $15 in tokens: (1/3) * (2/3) = 2/9.
Therefore, the probability that Bob will draw $15 in tokens is 2/9.
Find the area of the figure.
Answer:
98 ft ^2
Step-by-step explanation:
big triangle: (find the area of the space between)
bh/2
(14 x 14) /2 = 98
square: 14 x 14 = 196
196 - 98 = 98.
Use pythagorean theorem to solve the questions
Solve these problems:
A) 4y + 3 = 19
B) (1/2)n-3=5
Step-by-step explanation:
a 4y=19-3
4y=16
y=16/4
y=4
b. 1/2n=5+3
1/2n=8
n=8×2 as 1/2 become on right so it become 2
n=16
Step-by-step explanation:
[tex]4y + 3 = 19 \\ 4y = 19 - 3 \\ 4y = 16 \\ \frac{4y}{4} = \frac{16}{4} \\ y = 4[/tex]
[tex]( \frac{1}{2} )n - 3 = 5 \\ \frac{n}{2 } - 3 = 5 \\ \frac{n}{2} = 5 + 3 \\ 2 \times \frac{n}{2} = 8 \times 2 \\ n = 16[/tex]
Using ur knowledge of fractions and the second power law, explain
Answer:
1
Step-by-step explanation:
according to the law of exponents a0 = 1. Similarly b0=1
Any number with an exponent 0 will be a 1.
ASAP!!!!! !!
I need help, it’s urgent please!!!
Answer: A
Step-by-step explanation: Because if an ecosystem has a high biodiversity, then it’s most likely to survive things like an invasive species for example
A screen door spring has a spring constant of 188 N/m, and stretches 0.292 m when the door is opened. What force does it exert?
(Unit = N)
Answer:
The answer is 54.896N
Step-by-step explanation:
From Hooke's law,
Force = spring constant x extension
i.e
F = k x e
F = 188N/m x 0.292m
F = 54.896N
Answer:
54.846N
Step-by-step explanation:
Force = ?
Spring constant (K) = 188N/m
Spring stretch (x) = 0.292m
Force acting on a spring = spring constant * spring stretch
Force = 188 * 0.292
Force = 54.896N
The force acting on the spring is 54.896N
If you have 8 quarters and 9 dimes, what is the value of the
total amount in dollars?
Answer: $2.90
Step-by-step explanation:
Each quarter is worth 25 cents so we do 8x25 which is 200 and we do 9x10 which is 90 and when we add them up we get 290 cents which is 2.90 dollars
Answer:
$2.90
Step-by-step explanation:
8 times 25 equals 200 ($2)
9 times 10 equals 90 ($0.90)
what is the quotient for -20/ -10
Answer:
2
Step-by-step explanation:
To find the quotient you just divide the numerator (-20) by the denominator (-10)
-20 / -10 = 2
(The negatives cancel out!)
If the mean of the data set is 35 apples find the number of apples on the Granny Smith tree
35apples:
The number of apples on the Granny Smith tree can be found by looking at the mean of the data set, which in this case is 35 apples.
To determine the number of apples on the Granny Smith tree, just consider that the mean represents the average value of the data set.
Since the mean is 35, then you can conclude that there are 35 apples on the Granny Smith tree.
The number of apples in the Granny Smith tree is 41.
To find the number of apples in the Granny Smith tree, we can use the fact that the mean (average) of the data set is 35 apples. The mean is calculated by summing up all the values and dividing by the total number of values.
Let x be the number of apples in the Granny Smith tree.
The mean of the data set can be calculated as:
[tex]\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]For the given data set, the sum of all values is \( 34 + 29 + 36 + x \), and there are 4 values in total.[/tex]
So, we have the equation:
[tex]\[ 35 = \frac{34 + 29 + 36 + x}{4} \]Now, let's solve for \( x \):\[ 35 \times 4 = 34 + 29 + 36 + x \]\[ 140 = 99 + x \]\[ x = 140 - 99 \]\[ x = 41 \][/tex]
Therefore, the number of apples in the Granny Smith tree is 41.
Complete question:
The following table shows the number of apples on each apple tree in Craig’s backyard. If the mean of the data set is 35 apples, find the number of apples in the Granny Smith tree.
5. A salesman makes a salary of $350 per week. In addition, he makes 49
commission on his total sales. If he sells $1500, what was his total income
for the week? Remember...it's money.please write it that way. *
[tex]\text{We have to find the salesman's total salary for the week}\\\\\text{We know that he makes a base price of \$350 a week}\\\\\text{We also know he makes 4\% in commission from SALES}\\\\\text{From the given information, it says that he sold \$1500 worth of stuff}\\\\\text{Lets find his commission. To find this, we would multiply 1500 by 0.04:}\\\\1500*0.04=60\\\\\text{He makes \$60 in commission}\\\\[/tex]
[tex]\text{Now we need to find his total income for the week. To do this, add his}\\\text{salary and commission. Don't add how much he sells, he doesn't make}\\\text{money from that.}\\\\350+60=410\\\\\text{His income for the week was \$410}\\\\\boxed{\$410}[/tex]
Sales Tax in the state of Mathland is 8.5%. After buying school supplies, your total was $81.42, before tax. How much do you end up paying including tax? (SHOW WORK.)
A: $6.92
B: $74.50
C: $88.34
Answer:
A
Step-by-step explanation:
8.5% of 81.42
8.5 81.42 692.07
------- X ---------- = -------------
100 1 100
divide 692.07/100 which gives you 6.9207
if you round it to the nearest hundredth you get 6.92
Omar and Caleb each had a repair made on their cars. The initial cost of each repair is $1,000. Omar and Caleb each have two coupons. Each of them uses both of his coupons toward the cost of the repair. One coupon is for $80 off the repair cost. The other coupon is for 15% off the repair cost. Omar and Caleb use their coupons in a different order, as shown below. •Omar uses the $80 off the repair cost coupon first. He then uses the 15% off the repair cost coupon on the remaining balance. •Caleb uses the 15% off the repair cost coupon first. He then uses the $80 off the repair cost coupon on the remaining balance. Who paid the least amount of money for his car repair and how much less did he pay? Show all work HELP PLEASE SO I WON'T FAIL THEN I won't GET A CARRR
Answer:
Caleb paid $12 less
Step-by-step explanation:
Omar1. $80 off
$1000 - $80 = $9202. 15% off
$920- 15% = $920 * 0.85 = $782Omar paid for repair: $782
Caleb1. 15% off
$1000 - 15% = $1000*0.85 = $8502. $80 off
$850 - $80 = $770Caleb paid for repair: $770
As per above:
$782 - 770 = $12Caleb paid $12 less than Omar for his car repair.
Final answer:
Omar and Caleb had car repairs costing $1,000. By utilizing coupons differently, Caleb paid $12 less than Omar for the repair.
Explanation:
Omar and Caleb each had a repair made on their cars costing $1,000 initially. Omar used the $80 coupon first and then the 15% coupon. Caleb used the 15% coupon first and then the $80 coupon.
Omar: $1,000 - $80 = $920 remaining, then 15% off: $920 - 0.15*$920 = $782
Caleb: $1,000 - 0.15*$1,000 = $850 remaining, then $80 off: $850 - $80 = $770
Caleb paid less by $12 compared to Omar for his car repair.
Two pentagons are similar. So, their corresponding sides must have the same lengths.
TrueFalse
Answer:
False because they are similar not exactly alike.
if a circle has the radius 50cm what is the area
Step-by-step explanation:
I found it on Google, hopefully it's right
Which of the following is equivalent to the complex number i^80
The equivalent to the complex number i^80 is 1
How to determine the equivalent?The complex number is given as:
i^80
In complex numbers:
i^4 = 1
So, we have:
i^80 = (i^4)^20
Substitute i^4 = 1
i^80 = (1)^20
Evaluate
i^80 = 1
Hence, the equivalent to the complex number i^80 is 1
Read more about complex numbers at:
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please help I mark brainliest
Answer:
graph a
Step-by-step explanation:
y has to be less than the line
postive slope
the only graph that has both is graph a
Determine the missing information in the paragraph proof. Given: Lines a and c intersect at point S, creating 4 angles. Prove: Corresponding angles are congruent. Lines a and c intersect at point S. Line c is diagonal and also contains points R, Q, P. Line a is horizontal and also contains points U, T. We are given that lines a and c intersect at point S. Translate line a down line c until point S reaches point Q. Call the new line through Q line b. Because translations preserve orientation, lines a and b are ________. Because translations preserve angle measure, ∠RSU ≅ ∠RQU'. For the same reason, ∠RST ≅ ∠RQT', ∠PSU ≅ ∠PQU', and ∠PST ≅ ∠PQT'. Each of the angle pairs are corresponding angles. Therefore, corresponding angles are congruent. parallel perpendicular congruent reflected
Answer:
©The answer is Parallel
Step-by-step explanation:
Answer:
Parallel
Step-by-step explanation:
Find the GCF for the following list.
60, 14, 21
The GCF is
. (Simplify your answer.)
Answer:
The GCF if 60, 14, 21 is 1
A patient takes vitamin pills. Each day he must have at least 420 IU of vitamin A, 5 mg of vitamin
B1, and 60 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin A, 1
mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of
vitamin B7, and 15 mg of vitamin C. Pill 1 costs 30¢, and pill 2 costs 60¢. Complete parts a and b
below.
Final Answer:
Pill 1 is more cost-effective, meeting or exceeding daily requirements for vitamins A, B1, and C with lower cost (30¢) compared to pill 2 (60¢). It provides 480 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C with fewer pills, making it the optimal choice.
Step-by-step explanation:
The patient's daily requirements are 420 IU of vitamin A, 5 mg of vitamin B1, and 60 mg of vitamin C. Let's evaluate the contribution of each pill to these requirements.
Pill 1 provides 120 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C.
Pill 2 provides 60 IU of vitamin A, 1 mg of vitamin B7, and 15 mg of vitamin C.
To meet the vitamin A requirement, the patient can take 4 pills of type 1 (4 * 120 IU = 480 IU), while it would take 7 pills of type 2 (7 * 60 IU = 420 IU). So, pill 1 is more efficient for meeting the vitamin A requirement.
For vitamin B1, both pills contribute 1 mg each, and since the requirement is 5 mg, the patient needs to take 5 pills of either type.
For vitamin C, the patient needs 60 mg. Pill 1 provides 10 mg per pill, so 6 pills are needed (6 * 10 mg = 60 mg). Pill 2 provides 15 mg per pill, so 4 pills are needed (4 * 15 mg = 60 mg).
Considering the cost, pill 1 costs 30¢, and pill 2 costs 60¢. Since both pills are equally effective in meeting the B1 requirement and pill 1 is more efficient for vitamin A and equally efficient for vitamin C, the patient should choose pill 1 due to its lower cost.
How many customers were kept on hold for less than 25 seconds?
Answer:
54 customers
Step-by-step explanation:
Add them all together:
9 + 9 + 0 + 1 + 2 + 5 + 6 + 3 + 5 + 9 + 0 + 5
= 18 + 3 + 11 + 8 + 14
= 32 + 22
= 54
Answer: 54 Customers
Step-by-step explanation: From what i can see, it shows 3 sets of customers, all the seconds added together would be 54
9 + 9 = 18
0 + 1 + 2 + 5 + 6 = 14
3 + 5 + 9 = 17
0 + 5 = 5
now, add it all together
18 + 14 + 17 + 5 = 54
Explain step by step how you factor:
6x^2+ 11x + 3
Answer:
6x^2+ 11x + 3
= (3x +1) (2x +3)
Step-by-step explanation:
Math Term Definition. Factor. To factor a number means to break it up into numbers that can be multiplied together to get the original number. EXAMPLES: 6 = 3 x 2 so, factors of 6 are 3 and 2 9 = 3 x 3 so, factors of 9 are 3 and 3 Sometimes, numbers can be factored into different combinations.
In the diagram, angle abc is a right angle. Find the value of x
Show full working out pls ty
Answer:
x = 3.75
Step-by-step explanation:
ABC is a right angled triangle.
Therefore, by Pythagoras theorem:
[tex] {(10 - x)}^{2} = {x}^{2} + {5}^{2} \\ 100 - 20x + {x}^{2} = {x}^{2} + 25 \\ 100 - 20x = 25 \\ - 20x = 25 - 100 \\ - 20x = - 75 \\ x = \frac{ - 75}{ - 20} \\ \: \: \huge \red { \boxed{x = 3.75}}[/tex]
what’s the missing angle
Answer:
86°
Step-by-step explanation:
The total of all of the angles needs to add up to 180 degrees.
45 + 49 = 94
180 - 94 = 86 degrees
Answer:
86
Step-by-step explanation:
What is the equation of a line with a -y-intercept of -5 and a slope of 8.
a. y=8x+5
b .y=8x-5
c. y=-5x+8
d. y=-5x-8
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 8 and c = - 5, thus
y = 8x - 5 → B
Answer:
B
Step-by-step explanation:
y = mx + b
m represents slope and b is the y intercept
so 8x is mx in this equation and -5 is b
Can someone check this if it is right or wrong
A cone has a volume of 75 pie and a height of 9 cm.
What is the cone's diameter?
Enter your answer in the box.
Answer:
Volume of the cone is given by
[tex]V = \frac{\pi {r}^{2}h }{3} = 75\pi[/tex]
[tex] = > \frac{\pi {r}^{2}9 }{3} = 75\pi[/tex]
[tex] = > {r}^{2} = \frac{75\pi}{\pi \times 3} = 25[/tex]
[tex] = > r = \sqrt{25} = 5[/tex]
Diameter of the cone = 2×5 cm = 10 cm
How much would $300 invested at 7% interest compounded continuously be
worth after 4 years? Round your answer to the nearest cent.
A. $306.53
B. $384.00
C. $396.93
D. $347.09
Answer:
Hi there
The formula of compounded continuously is
A=pe^rt
A future value?
P present value 300
R interest rate 0.07
T time 4 years
E constant
So
A=300×e^(0.07×4)
A=396.932 round your answer to get
A=396.93
Good luck!
Step-by-step explanation:
six more than the product of four times the difference between x and 3
When x=8
Answer:
26
Step-by-step explanation:
Six more than four times the difference between x and 3
6+4(x-3)
And x is said to be 8
So let's substitute
6+4(8-3)
6+4(5)
6+20
26
So the final answer is 26
Answer: 26
Step-by-step explanation:
Find the median, lower quartile, and upper quartile for the set of data. 4, 1, 11, 8, 2, 9, 7, 6, 10, 5 Median = Lower quartile = Upper quartile =
Answer:
the answer is 6.5, 4, and 9.
Step-by-step explanation:
The median is 6.5.
The lower quartile is 4.
The upper quartile is 9.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
To find the median, we need to first put the data in order:
1, 2, 4, 5, 6, 7, 8, 9, 10, 11
There are 10 numbers in the data set, so the median is the average of the two middle numbers:
Median = (6 + 7)/2 = 6.5
To find the lower quartile, we need to find the median of the lower half of the data set: 1, 2, 4, 5, 6
There are 5 numbers in the lower half, so the median is the middle number:
Lower quartile = 4
To find the upper quartile, we need to find the median of the upper half of the data set: 7, 8, 9, 10, 11
There are 5 numbers in the upper half, so the median is the middle number:
Upper quartile = 9
Thus,
The median, lower quartile, and upper quartile are 6.5, 4, and 9.
Learn more about median here:
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Which steps should be used to compare the fractions 2 Over 9 and 5 Over 6?
Answer: 2/9 5/6
Step-by-step explanation:
Find the common denominator