There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced by half every 4 hours. What will be the population in 24 hours
1,094 bacteria
Step-by-step explanation:There are 6 periods of 4 hours in 24 hours, so the population will be multiplied by 1/2 6 times. That is, it will be multiplied by (1/2)^6 = 1/64.
The population then will be ...
... 70,000/64 ≈ 1094
Brenda said that the number 2 is prime because it has only two factors. Carla said that the number 2 is composite because it is even, and all even numbers are composite. Who is correct? A) Brenda is correct. B) Carla is correct. C) Both of them are correct. D) Neither of them is correct.
Answer:
a) brenda is right
Step-by-step explanation:
five prime numbers: 2, 3, 5, 7 and 11. A prime number is an integer, or whole number, that has only two factors — 1 and itself
Write an expression for
Answer: 6x - 18 (choice C)
Angle TSR is the same as angle RST. The order of the letters doesn't matter as long as the middle letter is the same (known as the vertex point).
Segment SQ bisects angle RST, so that means the two smaller pieces (angle TSQ and angle RSQ) are exactly half in measure compared to angle RST. Put another way, angle RST is twice that of angle RSQ
So,
angle RST = 2*(angle RSQ)
angle RST = 2*(3x - 9)
angle RST = 2*(3x) + 2*(-9)
angle RST = 6x - 18
HELP MEEEEEEEEEEE PLEASE!
Answer:
55,900 cm²
Step-by-step explanation:
The area of a triangle is half the product of its base and height.
... A = (1/2)·b·h
... = (1/2)(430 cm)(260 cm)
... = 55,900 cm²
The table shows the total distance (d), in kilometers, a bicycle traveled after t hours.
Time in hours (t) Distance in kilometers (d)
(t) (d)
0 0
1 8
2 16
Which equation shows the relationship between d and t?
d=8t
d=16t
d=t+8
d=t+16
Answer:
d = 8t
Step-by-step explanation:
Neither of the "t + ..." answers work for t=0. The d=16t answer does not work for t ≠ 0. The only choice that works for all of the table values is ...
... d = 8t
Someone please help I don’t understand
Answer:
D 2n+2
Step-by-step explanation:
We can check the slope of the function
m = (y2-y1)/(x2-x1)
= (10-8)/(4-3)
= 2/1
The slope is 2
We can use the point slope form of a line to calculate the equation for a line
y-y1 = m(x-x1)
y-2 = 2(x-2)
Distribute
y-6=2x-4
Add 6 to each side
y-6+6 = 2x-4+6
y = 2x+2
I'll GIVE BRAINLIEST!
y=-( (sqrt(x+2)) /(x/2-3) )^2 + 8
Find the domain and range
Domain
The argument of the square root function must be non-negative, so ...
... x+2 ≥ 0
... x ≥ -2
The denominator cannot be zero, so there is a disallowed value of x at ...
... x/2 -3 = 0
... x/2 = 3
... x = 6 . . . . . . . . . excluded from the domain
Range
The value of the expression is 8 for x=-2. As x approaches 6, the value of y approaches -∞.
Because the denominator is squared (has an even exponent), the sign does not change as x crosses 6, so function values increase from -∞ toward the horizontal asymptote at y=8.
Thus the range is (-∞, 8].
Which number completes the Pythagorean Triple of 14, 48, x?
50
Step-by-step explanation:These numbers are double those of the (7, 24, 25) triple. 2×25 = 50.
You can also figure it out from ...
... x = √(14² +48²) = √(196 +2304) = √2500 = 50
A quintic polynomial has, at most, how many x-intercepts?
3
4
5
6
Answer:
5 x-intercepts at most.
Step-by-step explanation:
Polynomial function with degree of 5
End behavior: falls to the left and rises to the right OR falls to the right and rises to the left .
Can have 0,1,2,3 or 4 turning points; can have
0,1,2,3,4 or 5 x-intercepts
A quintic polynomial, which is of degree 5, can have at most 5 x-intercepts as per the Fundamental Theorem of Algebra.
Explanation:A quintic polynomial is a polynomial of degree 5. According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n roots, or solutions. However, not all roots necessarily represent x-intercepts, as some might be complex roots.
On a graph, x-intercepts are points where the polynomial touches or crosses the x-axis, corresponding to the real roots of the polynomial equation. So, in general, a quintic polynomial will have at most 5 x-intercepts. This is because a polynomial of degree n can intersect the x-axis at most n times.
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Can someone pls help me. Find the illegal values of c in the multiplication statement.
Answer:
c ∈ {-7, -3, 2, 5}
Step-by-step explanation:
"Illegal" values are those values that make the expression undefined—that is, they make the denominator zero.
The denominator of the product factors as (c+7)(c-2)(c-5)(c+3), so the values of c that will make this product zero are ones that make the factors zero:
... c = -7, +2, +5, -3
_____
Comment on factoring
Each of the quadratics is factored by finding two factors of the constant whose sum is the coefficient of the linear term. You want ...
... factors of -14 = -1·14 = -2·7 . . . . that add to give +5. They are -2 and 7, so the quadratic factors as (c-2)(c+7)
... factors of -15 = 1·(-15) = 3·(-5) . . . . that add to give -2. They are 3 and -5, so the quadratic factors as (c+3)(c-5).
D 0,-2(x, y)(3, 5). The point (x, y) is: (1, 3) (-3/2, -5/2) (-6, -10)
Answer:
(-3/2, -5/2)
Step-by-step explanation:
When a point is dilated about the origin, each coordinate value is multiplied by the dilation factor. You seem to have ...
... -2x = 3 ⇒ x = -3/2
... -2y = 5 ⇒ y = -5/2
_____
In each case, you solve the linear equation by dividing by the coefficient of the variable.
Travis spent 20 minutes getting ready for school in the morning. He spent 9/20 of the time eating breakfast. Write this fraction of time as a decimal
Answer:
0.45
Step-by-step explanation:
9/20=0.45
Travis spent 9/20, which in decimal form is 0.45, of his 20-minute preparation time eating breakfast, which is equivalent to 9 minutes.
Travis spent a total of 20 minutes getting ready for school. Out of this time, he spent 9/20 of it eating breakfast. To express this fraction of time as a decimal, we simply perform division: 9 divided by 20.
9 / 20 = 0.45
Therefore, Travis spent 0.45 of the 20 minutes, or 45% of his preparation time, eating breakfast. When converting this to minutes, 0.45 * 20 minutes equals 9 minutes. Thus, Travis spent 9 minutes eating breakfast.
Drinking 7 fluid ounces of milk provides 236.25 milligrams of calcium. How many fluid ounce of milk are required tho prove 67.5 milligrams of calcium. Round to the nearest tenth
A.1.7 fluid ounces
B.2.0 fluid ounces
C.2.5 fluid ounces
D.2.3 fluid ounces
Answer:
Option B is correct.
2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the given statement: Drinking 7 fluid ounces of milk provides 236.25 milligrams of calcium.
Let x be the fluid ounce of milk.
then, by using proportion method we have;
[tex]\frac{7}{236.25} = \frac{x}{67.5}[/tex] ......[1]
Cross multiply states that an equation of fractions when each side consists of a fraction with a single denominator by multiplying the numerator of each side by the denominator of the other side and then, equating the two products obtained.
Apply cross multiply in [1];
[tex]7 \times 67.5 = 236.25 \times x[/tex]
Simplify:
[tex]472.5 = 236.25x[/tex]
Divide 236.25 we get;
[tex]x = \frac{472.5}{236.25}[/tex]
Simplify:
x = 2.0
therefore, 2.0 fluid ounces of milk are required to provide 67.5 milligrams of calcium
Solve the equation for the variable. Show each step of your solution process.
Answer:
x = 12
Step-by-step explanation:
√(x + 4) - 3 = 1 Add 3 to each side
√(x + 4) = 4 Square each side
x + 4 = 16 Subtract 4 from each side
x = 12
=====
Check:
√(12 + 4) – 3 = 1
√16 – 3 = 1
4 – 3 = 1
1 = 1
Answer:
Step-by-step explanation:
We have equation
[tex]\sqrt{x+4} -3=1[/tex]
to solve for x we first add 3 to both side
[tex]\sqrt{x+4}-3+3=1+3\\\sqrt{x+4} =4[/tex]
now we need to remove square root from left side, so we square both sides
[tex]x+4=4^{2}[/tex]
[tex]x+4=16[/tex]
now we subtract 4 from both sides
[tex]x+4-4=16-4\\x=12[/tex]
Joshua solved this problem. He says the answer is 489 yards. Joshua had 359 yards of his fishing line in the water. Then he reeled in 113 yards of his line from the water. How much of Joshua’s fishing line was still in the water? Solve the problem. Is Joshua’s answer reasonable?
The correct answer to the subtraction problem is 246 yards of Joshua's fishing line remaining in the water after reeling in 113 yards out of 359 yards. Joshua's initial answer of 489 yards is incorrect.
The student is asking for verification of Joshua’s solution to a subtraction problem that involves determining how much fishing line remains in the water after some has been reeled in. Joshua initially had 359 yards of line in the water and reeled in 113 yards. To find the remaining length of the line in the water, we subtract the length of the line reeled in from the initial length.
Step-by-Step Explanation
Start with the initial length of the fishing line in the water: 359 yards.
Subtract the length of the line that was reeled in: 113 yards.
Perform the subtraction: 359 yards - 113 yards = 246 yards.
So, the length of the fishing line that remained in the water was 246 yards.
Joshua’s answer of 489 yards is not reasonable because it does not reflect the correct subtraction (359 - 113 = 246). The correct answer is 246 yards still in the water.
2. At Fly-Right Airlines, passengers are informed that checked bags must weigh 40 lb or less, or they will have to pay a fee for an oversized bag. (a) Write an inequality that represents the weight of a checked bag that will not result in a fee. Let w represent the weight of the bag. (b) Are there any solutions to the inequality that do not make sense for this situation? Explain.
Answer:
see below
Step-by-step explanation:
a) w <= 40 lbs
b) Do you have any bag that weigh 0 lbs or negative lbs?
We need to rewrite the inequality so that these are not there
0<= w <= 40 lbs
He daily milk production of guernsey cows is approximately normally distributed with a mean of 35 kg/day and a standard deviation of 6 kg/day. the producer is concerned when the mild production of a cow falls below the 5th percentile because the animal may be ill. the 5th percentile (in kg) of the daily milk production is approximatley:
Answer:
25.1 kg
Step-by-step explanation:
A suitable probability calculator can tell you the 5th percentile of this distribution.
Cameron is going to the carnival. The price of admission to the carnival is $6.50, and each ride costs an additional 0.75 cents. If Cameron can spend at most $20.00 at the carnival, which inequality represents all the possible values of r rides Cameron can go on? A) 0.75 + 6.50r ≤ 20.00 B) 0.75 + 6.50r ≥ 20.00 C) 6.50 + 0.75r ≤ 20.00 D) 6.50 + 0.75r ≥ 20.00
r = the number of rides
0.75r + 6.50 ≤ 20.00
[They charge $0.75 per ride (r) plus an admission fee of $6.50, and he can spend at most (maximum) $20. This means that he can spend $20 or less]
Your answer is C
Answer:
Option C is the correct answer.
Step-by-step explanation:
The price of admission to the carnival is $6.50.
Cost per ride = 0.75
Money Cameron having = 20 $
Let the number of rides be r, he cannot spend more than 20 $
That is
6.50 + 0.75 r ≤ 20.00
Option C is the correct answer.
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Try this option. Answer: 72+18π
Step-by-step explanation:
Formula is:
Area= 2*Area_of_two_squares + 1/2 *Area_of_the_circle, where
Area_of_1_square=6*6=36 cm²;
Area_of_the_circle=π*6²=36π cm²;
finally, according to the formula above Area=2*36+0.5*36π=72+18π
Answer:
Step-by-step explanation:
72+18pi
Donovan eats 2 granola bars and drinks 1 glass of orange juice for breakfast every day. The price of a granola bar is B dollars and the price of a glass of orange juice is J dollars. The expression 7(2B+J) describes how much Donovan spends on breakfast in one week. What does 2B represent in the expression?
Answer:
# of granola bars and it's cost.
Step-by-step explanation:
It is asking for the meaning of 2B. Note that inside the question, it states that:
"The price of a granola bar is B dollars".
It also states that:
"Donovan eats 2 granola bars".
This means that to solve for the total spent on granola bars, you multiply the price (B) with the amount gotten (2 in this case).
~
Answer:
2B
Step-by-step explanation:
Means the amount Donovan spends on granola bars each day. Since he has 2 granola bars and the price is B dollars.
Determine the slope of the line that is perpendicular to the line y = -7x - 12.
Select one:
A. 17
B. −3
C. −7
D. −12
A. 1/7
Step-by-step explanation:The slope of the given line is the coefficient of x, -7. The slope of a perpendicular line will be the opposite reciprocal of that:
... -1/(-7) = 1/7 . . . . . seems to match selection A
_____
Comment on the answer choices
We assume this question suffers from a problem seen often on Brainly where questions and/or answers are copied and pasted without any follow-up editing to make sure the copy is faithful. Often, math symbols are special characters that get filtered out in the process.
The fraction bar commonly comes up missing. Here, that makes 1/7 look like 17, which makes the correct answer look like "none of the above."
m∥n, m∠1 = 50°, m∠2 = 48°, and line s bisects ∠ABC. What is m∠3?
49°
Step-by-step explanation:∠DEF = ∠1 +∠2 = 50° +48° = 98°
∠ABC = ∠DEF because they are alternate exterior angles, hence congruent.
∠3 = ∠4 because they are vertical angles.
∠3 = (1/2)∠ABC = (1/2)·98° . . . . . ∠4 is half of ∠ABC
∠3 = 49°
i need help plz plz plz help me. ASAP. and plz type your reasoning.
C = 2.00r +20
Step-by-step explanation:The coefficient is the multiplier of r, the cost of each ride. If it has gone down by $0.50, then its new value is ...
... 2.50 -0.50 = 2.00
The constant in the equation is the initial cost of the wristband. It is the value of C when r=0. If it has gone up by $5, its new value is ...
... 15 + 5 = 20
Write an expression as a monomial in a standard form:
−5x^3·y^2·5x^2·y^3
Answer:
-25x⁵y⁵
Step-by-step explanation:
Coefficients include (-5)(5) = -25
x-factors include (x^3)(x^2) = x^5
y-factors include (y^2)(y^3) = y^5
Then the product is ...
... -25x^5·y^5
Geo usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day. If he starts drinking 64 ounces, what is the percent increase? Round to the nearest percent.
78%
Step-by-step explanation:The percentage change is calculated from ...
... percent change = ((new amount) -(old amount))/(old amount) × 100%
... = (64 -36)/36 × 100%
... = 28/36 × 100%
... ≈ 0.78 × 100%
... ≈ 78%
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than a certain number of inches.
Sketch and label the sides of this rectangle. Use an algebraic expression to represent the length of the long sides.
Let x be the certain number of inches mentioned in the problem. So, three less than this quantity is [tex] x-3 [/tex]
This means that you have to sketch a rectangle labelling the short side with 2, and the long sides with [tex] x-3 [/tex]
4. The exchange rate of U.S. dollars to British pounds (£) is .63. You have $4000 to convert to British pounds. How many British pounds will you receive?
Answer:
£2,520
Step-by-step explanation:
The exchange rate of U.S. dollars to British pounds is .63. You have $4000 to convert to British pounds (?). 4,000 * .63 = 2,520. Therefore the amount of British pounds you will receive is: £2,520.
If ∠A is complementary to ∠B, and ∠C is complementary to ∠B, what can you conclude about ∠A and ∠C?
∠A ≅ ∠C
Step-by-step explanation:Angles complementary to the same angle are congruent to each other. Angles A and C are both complementary to angle B, hence they are congruent.
If angle A is complementary to angle B, and angle C is also complementary to angle B, then angles A and C must be equal. This is because complementary angles add up to 90 degrees.
Explanation:If ∠A is complementary to ∠B, and ∠C is also complementary to ∠B, then ∠A and ∠C are equal.
Complementary angles add up to 90 degrees. This means that ∠A + ∠B = 90° and ∠C + ∠B = 90°. Therefore, if ∠B is the same in both instances, it can be deducted that ∠A = ∠C because they are both equal to the remaining measure after subtracting ∠B from 90°.
In simpler terms, if you know that two different angles are both complementary to a same angle (∠B in this case), then those two angles must be equal to each other.
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In the figure, BCND is a rectangle and CGNR is a rhombus. The area of BCND is 90 and BC = 10. What is 3GR?
Answer:
[tex]3GR=27[/tex]
Step-by-step explanation:
Since area of rectangle BCND is given as 90 and one of its side is 10, the other side MUST be 9.
[tex]CN*BC=90\\CN*10=90\\CN=9[/tex]
In Rhombus CGNR, CN and GR are congruent (property of Rhombus). Hence GR = 9 as well.
Thus 3GR = 3(9) = 27
First answer choice is right.
HELP WITH ONE PLEASE!
Amy can ride her bike 4 miles in 30 minutes. Sebastian can ride his bike 3 miles in 24 minutes. At her
24
current rate, what is the distance, in miles, Amy can ride her bike in 12 minutes?
(A) 1.6
(B) 2.5
(C) 3.0
(D) 9.0
Sally drives 66 miles in 3 hours and Molly drives 72 miles in 4 hours. What is the difference between
23
their average speeds, in miles per hour?
(A) 4
(B) 6
(C) 18
(D) 22
24. (A) 1.6
23. (A) 4
Step-by-step explanation:24.Amy's distance is proportional to the time spent riding, so in 12/30 of the time (12 minutes out of 30 minutes), she will ride 12/30 of the distance:
... (12/30)·(4 mi) = 48/30 mi = 1.6 mi
23.Sally's speed is (66 mi)/(3 h) = 22 mi/h. Molly's speed is (72 mi)/(4 h) = 18 mi/h.
The difference between their speeds is (22 -18) mi/h. = 4 mi/h.
Final answer:
A) 1.6 and A)4
Amy can ride her bike 1.6 miles in 12 minutes, and the difference in average speed between Sally and Molly is 4 mph.
Explanation:
To find the distance Amy can travel in 12 minutes, first determine her speed in miles per minute. Since Amy can ride her bike 4 miles in 30 minutes, her speed is 4 miles / 30 minutes = 0.1333 miles/minute. To find out how far she can go in 12 minutes, multiply her speed by the time: 0.1333 miles/minute x 12 minutes = 1.6 miles. Therefore, Amy can ride 1.6 miles in 12 minutes, which corresponds to answer choice (A).
Calculating the Difference in Average Speed
Sally's average speed is 66 miles / 3 hours = 22 mph, and Molly's average speed is 72 miles / 4 hours = 18 mph. The difference in their average speeds is 22 mph - 18 mph = 4 mph, which corresponds to answer choice (A).