Using an exponential function, it is found that the latest models battery life will be of 841 minutes 7 months from now.
<h3>What is an exponential function?</h3>
An increasing exponential function is modeled by:
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem, considering that the current battery life is of 684 minutes, and it should increase by 3% each month, the equation for the battery life after t months is given by:
Then, in 7 months, it will be given by:
More can be learned about exponential functions at brainly.com/question/25537936
Let the number of 4th and 5th graders be x.
The number of k-3 graders will be (x+300)
The fraction of 4th and 5th graders is 5/12
The fraction of the whole students combined is 1/1
The fraction of k-3 graders is 1-5/12=7/12
The total number of students will be x+(x+300)=2x+300
the fraction of 4th and 5th graders will be given by:
x/(2x+300)=5/12
12x=5(2x+300)
12x=10x+1500
2x=1500
x=1500/2=750
Thus the total number of students will be:
2x+300
=2*750+300
=1500+300
=1800
b] Given that of the 4th and 5th graders, (x=750), 2/5 are 4th graders, therefore the fraction of 5th graders will be:
1-2/5=3/5
the total number of 5th graders will be:
3/5*750
=450
The number of 5th graders will be 450
A set of data is given. It is required to find the first, second, and third quartile.
The given data is:
Recall that the lower quartile Q₁, or the first quartile, is the median of the lower half of the data in a set.
The lower half is:
Find the median of the lower half to get the first quartile, Q₁:
Hence, Q₁=9.
Recall that the second quartile Q₂ is the same as the median of the data.
The median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Notice that the middle number is 15.
Hence, second quartile Q₂=15.
The upper quartile Q₃, or the third quartile, is the median of the upper half of the data in a set.
The upper half of the data is:
Calculate the median to find the third quartile, Q₃:
It follows that Q₃=17
The complete table is shown below:
The two-column proof that shows that ΔEAB ≅ ΔDCB by SAS congruence theorem is explained below.
<h3>What is the the SAS Congruence Theorem?</h3>
The Side-angle-side congruence theorem (SAS) that states that two triangles that are have two pairs of corresponding congruent sides and a pair of included corresponding congruent angles are congruent to each other.
<h3>What is an Isosceles Triangle?</h3>
Any triangle with two equal base angles is referred to as an isosceles triangle, The sides opposite these base angles are also congruent to each other.
Given the diagram below, the proof is expressed as follows:
Statement 1: ΔEAB and ΔDCB are two right triangles
Reason 1: Given
Statement 2: ∠EAB ≅ DCB
Reason 2: Right angles
Statement 3: ∠BED ≅ BDE
Reason 3: Given
Statement 4: ΔBED is an isosceles triangle
Reason 4: Definition of isosceles triangle
Statement 5: BE ≅ BD
Reason 5: Definition of isosceles triangle
Statement 6: ΔEAB ≅ ΔDCB
Reason 6: SAS
Learn more about the SAS congruence theorem on:
brainly.com/question/2102943
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